A Graph-theoretic QoS-aware Vulnerability Assessment for Network Topologies
|
|
- Basil Flowers
- 6 years ago
- Views:
Transcription
1 A Graph-theoretic QoS-aware Vulnerability Assessment for Network Topologies March 24, 2010
2 Table of contents 1 Problem Definition and Contributions 2 3 network with small amount of constraints small networks with unrestricted constraints two fast heuristic algorithms for general networks 4
3 System Model given a networks with a set of s t paths; each path satisfies some of the constraints, thus has a satisfactory score by assigning each constraint a score. as long as there exists a path with score higher the some threshold, the network is still operational. goal: at least home many node/link failures will make the network not operational, i.e. no such satisfiable path exists, and QoS routing service is not available from s to t.
4 Graph Model directed graph G(V, E), source s, destination t; ( ) additive weight vector for each edge e j = (u, v) E: w j 1,wj 2,,wj m. ( weight vector for each path: ej p wj 1, ej p wj 2,, ej p m) wj ; constraint threshold vector (c 1,c 2,,c m); priority vector (λ 1, λ 2,, λ m); we define a satisfactory score φ(p) for path p as: where p i iff w p i c i φ(p) = λ j j:p i
5 Graph Model A (1,2) B (3,7) C (1,2) (2,2) (1,1) D (2,2) E (2,1) F (2,2) (1,1) (2,3) G (2,2) (3,2) H I Given a score threshold ρ, find the minimum number of edges whose removal makes φ(p) = max{φ(p) s t path p in G} ρ
6 Integer Program Variables: X e = 1 if edge e is NOT removed in the optimal solution, 0 otherwise; Y pi = 1 if a s t path p has w p i c i, 0 otherwise; a large constant ǫ = max i { e E we i }.
7 Integer Program min s.t. (1 X e) e E m i=1 Y piλ i ρ, s t path p e p we i ǫ Y pi ǫ + e p (1 Xe)ǫ + c i, i,p e p we i > 1 Y pi ǫ e p (1 Xe)ǫ + c i, i,p X e [0,1] Y pi [0,1] Figure: Integer Programming Formulation
8 Main Contributions provide the first graph-theoretic QoS-ware vulnerability assessment method; abstract the assessment problem as a graph optimization problem and study its hardness; present exact solutions to the problem in two practical cases and several heuristics for general cases.
9 decide version Given a set of edges deleted, does there exist a path P satisfying φ(p) ρ in the remaining graph. Definition (QoS-SP) Given a graph with an m-dimension constraint vector, find a path P such that φ(p) = max φ(p) p=[s,,t] G Definition (MCP) Given m constraints C i, the problem is to find a path P from a source node s to a destination node t such that w i (P) w i (u, v) C i (u,v) P for all i [1, m]
10 NP-hard Lemma QoS-SP problem is NP-Complete. Proof. Consider the decision version of QoS-SP: given a positive number k, decide if there exists a path P with φ(p) k. This proof is straightforwardly by reduction from MCP problem by letting k = m i=1 λ i. Then if there exists a solution for the QoS-SP problem, then the path is a feasible path to MCP, otherwise, MCP has no solution. Since MCP is NP-hard, the proof completes.
11 network with small amount of constraints small networks with unrestricted constraints two fast heuristic algorithms for general networks Exact Solution Enumerate all (up to 2 m ) satisfiable constraint states; Employ FringeMCSP [5] to find the shortest path that satisfies a specific set of constraints; Use revised Edmonds-Karp algorithm to remove all satisfiable augmenting path, w.r.t a set of constraints. Find a minimum set of edge cut.
12 network with small amount of constraints small networks with unrestricted constraints two fast heuristic algorithms for general networks Exact Solution Exact Algorithm S ; for any maximal subset ss of M with c i ss λ i < ρ do S S {M \ ss} while S do ss extracted from S; for each edge (i,j) E do Set f (i,j) = f (j,i) = 0; Set c f (i,j) = 1 and c f (j, i) = 0; while shortest path q that satisfies all constraints in ss can be found using FringeMCSP do for each edge (u, v) q do c f (q) = min{c f (u, v) : (u, v) q}; f (u, v) = f (u, v) + c f (q); f (v,u) = f (u, v); c f (u, v) = c(u, v) f (u, v); c f (v, u) = c(v, u) f (v,u); all the vertices reachable from s on the residual network induces a cut T. Return the minimum cut among the cuts derived.
13 network with small amount of constraints small networks with unrestricted constraints two fast heuristic algorithms for general networks Exact Solution Enumeration of satisfiable constraint states does not work. Exact Solution: Employ an existing all-path dynamic programming algorithm label-correcting [3] to discovery satisfiable paths; Use revised Edmonds-Karp algorithm [6] to return the cut.
14 network with small amount of constraints small networks with unrestricted constraints two fast heuristic algorithms for general networks Label-Correcting Label-Correcting to find satisfiable paths S ; labelset(s) {(0, 0,, 0, )}; Q {s}; while Q do u extracted from the end of Q; for all outgoing edges (u, v) do labellist (v) Merge(labelList(v), labellist(u), (u, v)); /*extend tuples of u to v by adding the weights of (u, v), eliminate all dominated tuples.*/ if labellist (v) labellist(v) then labellist(v) labellist (v), Q Q {v}; S all the PO paths obtained from labellist(t); Return q = max p{φ(p) p S}.
15 network with small amount of constraints small networks with unrestricted constraints two fast heuristic algorithms for general networks Strategies Adopt a Relax-SAT test for estimate the existence of satisfiable path in the remaining graph; Adopt two greedy metrics to iteratively remove edges until the Relax-SAT test returns Negative result.
16 network with small amount of constraints small networks with unrestricted constraints two fast heuristic algorithms for general networks Relax-SAT test Relax-SAT Metric For each edge e, For each path p, ϕ 1 (e) = m i=1 w e i c i λ i ϕ 1 (p) = e p ϕ(e) Similarly, define ϕ 2 (e) = m i=1 w e i c i λ i
17 network with small amount of constraints small networks with unrestricted constraints two fast heuristic algorithms for general networks How far from SAT Assume λ m i λ i, β(p) max i ( wp c i ); Assume p satisfies a set C s of constrains, and does not satisfy the set C s, then φ(p) = c i C s λ i and ϕ 1 (p) = w p i c i C s λ c i w j i c j C s λ c j, therefore j φ(p) ρ ϕ 1 (p) ρ (λ ρ)β(p); ϕ 1 (p) ρ φ(p) ρ; since it is hard to calculate β(p) when p is not determinate, we assert maxϕ 1 (p) = minϕ 2 (p) ρ maxφ(p) ρ; minϕ 2 (p) ρ maxφ(p) ρ; p
18 network with small amount of constraints small networks with unrestricted constraints two fast heuristic algorithms for general networks Relax-SAT test Relax-SAT test Input: directed graph G = (V, E), constant ρ; Output: is there a satisfiable path. for every edge e E do ϕ 2 (e) m wi e i=1 λ c i ; i q shortest s-t path on metric ϕ 2 ; if ϕ 2 (q) > ρ then Return NO; if ϕ 2 (q) < ρ then Return YES;
19 network with small amount of constraints small networks with unrestricted constraints two fast heuristic algorithms for general networks Two greedy metrics Definition (Nonlinear Mixed Edge Metric) n ( ) wi (e)π(i, e) α ξ(e) = λ i c i=1 i where w i (e) is the i th weight on edge e, π(i,e) is the length of a s t path, which has the minimum weight w.r.t the i th constraint over all s t paths containing e, and λ i is the priority parameter for the i th constraint. It is evident that the smaller ξ(e) is, the more likely it will be included in the QoS-optimal path. α [1,, + ) is tuned to increase the likelihood of this path to be selected in the optimal solution.
20 network with small amount of constraints small networks with unrestricted constraints two fast heuristic algorithms for general networks Two greedy metrics Definition (Betweenness) θ(e) i: e P i λ i where P i refer to the shortest path w.r.t the i th constraint.
21 Results To be announced.
22 Bibliography Fernado A. Kuipers and Piet F. A. Van Mieghem, Conditions that Impact the complexity of QoS Routing, IEEE transaction on Networking, 2005 Line B. Reinhardt and David Pisinger, Multi-Objective and Multi-Constrained Non-Additive Shortest Path Problems, Technique Report, DTU Management, Turgay Korkmaz and Marwan Krunz, Multi-Constrained Optimal Path Selection, Infocom, P. Kh adivi, S. Samavi and T. D. Todd, Multi-constraint QoS routing using a new single mixed metrics, Journal of Network and Computer Applications, Yuxi Li, Janelee Harms, Robert Holte, Fast Exact MultiConstraint Shortest Path Algorithms, ICC, Jack Edmonds and Richard M. Karp, Theoretical improvements in algorithmic efficiency for network flow problems, Journal of the ACM 19 (2):
Maximum Flow. Flow Networks. Flow Networks Ford-Fulkerson Method Edmonds-Karp Algorithm Push-Relabel Algorithms. Example Flow Network
Flow Networks Ford-Fulkerson Method Edmonds-Karp Algorithm Push-Relabel Algorithms Maximum Flow Flow Networks A flow network is a directed graph where: Each edge (u,v) has a capacity c(u,v) 0. If (u,v)
More informationTraveling Salesman Problem (TSP) Input: undirected graph G=(V,E), c: E R + Goal: find a tour (Hamiltonian cycle) of minimum cost
Traveling Salesman Problem (TSP) Input: undirected graph G=(V,E), c: E R + Goal: find a tour (Hamiltonian cycle) of minimum cost Traveling Salesman Problem (TSP) Input: undirected graph G=(V,E), c: E R
More informationMaximum flows & Maximum Matchings
Chapter 9 Maximum flows & Maximum Matchings This chapter analyzes flows and matchings. We will define flows and maximum flows and present an algorithm that solves the maximum flow problem. Then matchings
More informationSolution for Homework set 3
TTIC 300 and CMSC 37000 Algorithms Winter 07 Solution for Homework set 3 Question (0 points) We are given a directed graph G = (V, E), with two special vertices s and t, and non-negative integral capacities
More informationMathematical Tools for Engineering and Management
Mathematical Tools for Engineering and Management Lecture 8 8 Dec 0 Overview Models, Data and Algorithms Linear Optimization Mathematical Background: Polyhedra, Simplex-Algorithm Sensitivity Analysis;
More informationToward the joint design of electronic and optical layer protection
Toward the joint design of electronic and optical layer protection Massachusetts Institute of Technology Slide 1 Slide 2 CHALLENGES: - SEAMLESS CONNECTIVITY - MULTI-MEDIA (FIBER,SATCOM,WIRELESS) - HETEROGENEOUS
More informationLECTURES 3 and 4: Flows and Matchings
LECTURES 3 and 4: Flows and Matchings 1 Max Flow MAX FLOW (SP). Instance: Directed graph N = (V,A), two nodes s,t V, and capacities on the arcs c : A R +. A flow is a set of numbers on the arcs such that
More informationClustering-Based Distributed Precomputation for Quality-of-Service Routing*
Clustering-Based Distributed Precomputation for Quality-of-Service Routing* Yong Cui and Jianping Wu Department of Computer Science, Tsinghua University, Beijing, P.R.China, 100084 cy@csnet1.cs.tsinghua.edu.cn,
More informationApproximability Results for the p-center Problem
Approximability Results for the p-center Problem Stefan Buettcher Course Project Algorithm Design and Analysis Prof. Timothy Chan University of Waterloo, Spring 2004 The p-center
More informationGraphs and Network Flows IE411. Lecture 13. Dr. Ted Ralphs
Graphs and Network Flows IE411 Lecture 13 Dr. Ted Ralphs IE411 Lecture 13 1 References for Today s Lecture IE411 Lecture 13 2 References for Today s Lecture Required reading Sections 21.1 21.2 References
More informationQuality of Service Routing
Quality of Service Routing KNOM Tutorial 2004, Jeju, Korea, Nov. 4-5, 2004. November 5, 2004 Kwang-Hui Lee Communication Systems Lab, Changwon National University khlee@changwon.ac.kr Contents Introduction
More informationA Heuristic Algorithm for the Multi-constrained Multicast Tree
A Heuristic Algorithm for the Multi-constrained Multicast Tree Wen-Lin Yang Department of Information Technology National Pingtung Institute of Commerce No.51, Ming-Sheng East Road, Pingtung City,Taiwan
More informationComputing a Path subject to Multiple Constraints: Advances and Challenges
Computing a Path subject to Multiple Constraints: Advances and Challenges Guoliang (Larry) Xue Faculty of Computer Science and Engineering School of Computing, Informatics and Decision Systems Engineering
More informationAn Evolutionary Algorithm for the Multi-objective Shortest Path Problem
An Evolutionary Algorithm for the Multi-objective Shortest Path Problem Fangguo He Huan Qi Qiong Fan Institute of Systems Engineering, Huazhong University of Science & Technology, Wuhan 430074, P. R. China
More informationChapter 5 Graph Algorithms Algorithm Theory WS 2012/13 Fabian Kuhn
Chapter 5 Graph Algorithms Algorithm Theory WS 2012/13 Fabian Kuhn Graphs Extremely important concept in computer science Graph, : node (or vertex) set : edge set Simple graph: no self loops, no multiple
More information1 The Traveling Salesperson Problem (TSP)
CS 598CSC: Approximation Algorithms Lecture date: January 23, 2009 Instructor: Chandra Chekuri Scribe: Sungjin Im In the previous lecture, we had a quick overview of several basic aspects of approximation
More informationPerformance Evaluation of Constraint-Based Path Selection Algorithms
Performance Evaluation of Constraint-Based Path Selection Algorithms Fernando Kuipers, Delft University of Technology Turgay Korkmaz, University of Texas at San Antonio Marwan Krunz, University of Arizona
More informationConnected Liar s Domination in Graphs: Complexity and Algorithm 1
Applied Mathematical Sciences, Vol. 12, 2018, no. 10, 489-494 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ams.2018.8344 Connected Liar s Domination in Graphs: Complexity and Algorithm 1 Chengye
More informationA Randomized Algorithm for Minimizing User Disturbance Due to Changes in Cellular Technology
A Randomized Algorithm for Minimizing User Disturbance Due to Changes in Cellular Technology Carlos A. S. OLIVEIRA CAO Lab, Dept. of ISE, University of Florida Gainesville, FL 32611, USA David PAOLINI
More informationAn Introduction to Dual Ascent Heuristics
An Introduction to Dual Ascent Heuristics Introduction A substantial proportion of Combinatorial Optimisation Problems (COPs) are essentially pure or mixed integer linear programming. COPs are in general
More informationCross-Virtual Concatenation for Ethernet-over-SONET/SDH Networks
Cross-Virtual Concatenation for Ethernet-over-SONET/SDH Networks Satyajeet S. Ahuja and Marwan Krunz {ahuja,krunz}@ece.arizona.edu Dept. of Electrical and Computer Engineering, The University of Arizona.
More information2.3 Optimal paths. Optimal (shortest or longest) paths have a wide range of applications:
. Optimal paths Optimal (shortest or longest) paths have a wide range of applications: Google maps, GPS navigators planning and management of transportation, electrical and telecommunication networks project
More informationThe Encoding Complexity of Network Coding
The Encoding Complexity of Network Coding Michael Langberg Alexander Sprintson Jehoshua Bruck California Institute of Technology Email: mikel,spalex,bruck @caltech.edu Abstract In the multicast network
More informationJessica Su (some parts copied from CLRS / last quarter s notes)
1 Max flow Consider a directed graph G with positive edge weights c that define the capacity of each edge. We can identify two special nodes in G: the source node s and the sink node t. We want to find
More informationGraphs and Network Flows IE411. Lecture 21. Dr. Ted Ralphs
Graphs and Network Flows IE411 Lecture 21 Dr. Ted Ralphs IE411 Lecture 21 1 Combinatorial Optimization and Network Flows In general, most combinatorial optimization and integer programming problems are
More informationComputer Science & Engineering 423/823 Design and Analysis of Algorithms
Computer Science & Engineering 423/823 Design and Analysis of Algorithms Lecture 07 Single-Source Shortest Paths (Chapter 24) Stephen Scott and Vinodchandran N. Variyam sscott@cse.unl.edu 1/36 Introduction
More informationComputational problems. Lecture 2: Combinatorial search and optimisation problems. Computational problems. Examples. Example
Lecture 2: Combinatorial search and optimisation problems Different types of computational problems Examples of computational problems Relationships between problems Computational properties of different
More informationLecture 10,11: General Matching Polytope, Maximum Flow. 1 Perfect Matching and Matching Polytope on General Graphs
CMPUT 675: Topics in Algorithms and Combinatorial Optimization (Fall 2009) Lecture 10,11: General Matching Polytope, Maximum Flow Lecturer: Mohammad R Salavatipour Date: Oct 6 and 8, 2009 Scriber: Mohammad
More informationReducing Directed Max Flow to Undirected Max Flow and Bipartite Matching
Reducing Directed Max Flow to Undirected Max Flow and Bipartite Matching Henry Lin Division of Computer Science University of California, Berkeley Berkeley, CA 94720 Email: henrylin@eecs.berkeley.edu Abstract
More informationCuts, Connectivity, and Flow
Cuts, Connectivity, and Flow Vertex Cut and Connectivity A separating set or vertex cut of a graph G is a set S V(G) such that G S G S has more than one component A graph G is k-connected if every vertex
More informationSyllabus. simple: no multi-edges undirected edges in-/out-/degree /0: absent 1: present (strongly) connected component subgraph, induced graph
Introduction to Algorithms Syllabus Recap on Graphs: un/directed, weighted Shortest Paths: single-source, all-pairs Minimum Spanning Tree: Prim, Kruskal Maximum Flow: Ford-Fulkerson, Edmonds-Karp Maximum
More informationIntroduction. I Given a weighted, directed graph G =(V, E) with weight function
ntroduction Computer Science & Engineering 2/82 Design and Analysis of Algorithms Lecture 05 Single-Source Shortest Paths (Chapter 2) Stephen Scott (Adapted from Vinodchandran N. Variyam) sscott@cse.unl.edu
More informationCSE 417 Network Flows (pt 3) Modeling with Min Cuts
CSE 417 Network Flows (pt 3) Modeling with Min Cuts Reminders > HW6 is due on Friday start early bug fixed on line 33 of OptimalLineup.java: > change true to false Review of last two lectures > Defined
More informationApproximation Algorithms
Approximation Algorithms Group Members: 1. Geng Xue (A0095628R) 2. Cai Jingli (A0095623B) 3. Xing Zhe (A0095644W) 4. Zhu Xiaolu (A0109657W) 5. Wang Zixiao (A0095670X) 6. Jiao Qing (A0095637R) 7. Zhang
More informationMinimum Spanning Tree (undirected graph)
1 Minimum Spanning Tree (undirected graph) 2 Path tree vs. spanning tree We have constructed trees in graphs for shortest path to anywhere else (from vertex is the root) Minimum spanning trees instead
More informationImportant separators and parameterized algorithms
Important separators and parameterized algorithms Dániel Marx 1 1 Institute for Computer Science and Control, Hungarian Academy of Sciences (MTA SZTAKI) Budapest, Hungary School on Parameterized Algorithms
More informationMaximum flow problem CE 377K. March 3, 2015
Maximum flow problem CE 377K March 3, 2015 Informal evaluation results 2 slow, 16 OK, 2 fast Most unclear topics: max-flow/min-cut, WHAT WILL BE ON THE MIDTERM? Most helpful things: review at start of
More informationMathematical and Algorithmic Foundations Linear Programming and Matchings
Adavnced Algorithms Lectures Mathematical and Algorithmic Foundations Linear Programming and Matchings Paul G. Spirakis Department of Computer Science University of Patras and Liverpool Paul G. Spirakis
More informationBi-directional Search in QoS Routing
Bi-directional Search in QoS Routing F.A. Kuipers and P. Van Mieghem Delft University of Technology Electrical Engineering, Mathematics and Computer Science P.O Box 5031, 2600 GA Delft, The Netherlands
More information9.1 Cook-Levin Theorem
CS787: Advanced Algorithms Scribe: Shijin Kong and David Malec Lecturer: Shuchi Chawla Topic: NP-Completeness, Approximation Algorithms Date: 10/1/2007 As we ve already seen in the preceding lecture, two
More informationIntroduction. I Given a weighted, directed graph G =(V, E) with weight function
ntroduction Computer Science & Engineering 2/82 Design and Analysis of Algorithms Lecture 06 Single-Source Shortest Paths (Chapter 2) Stephen Scott (Adapted from Vinodchandran N. Variyam) sscott@cse.unl.edu
More information2.3 Optimal paths. E. Amaldi Foundations of Operations Research Politecnico di Milano 1
. Optimal paths E. Amaldi Foundations of Operations Research Politecnico di Milano Optimal (minimum or maximum) paths have a wide range of applications: Google maps, GPS navigators planning and management
More informationGraph Algorithms Matching
Chapter 5 Graph Algorithms Matching Algorithm Theory WS 2012/13 Fabian Kuhn Circulation: Demands and Lower Bounds Given: Directed network, with Edge capacities 0and lower bounds l for Node demands for
More informationNP-Completeness. Algorithms
NP-Completeness Algorithms The NP-Completeness Theory Objective: Identify a class of problems that are hard to solve. Exponential time is hard. Polynomial time is easy. Why: Do not try to find efficient
More information1 Introduction. 2 The Generic Push-Relabel Algorithm. Improvements on the Push-Relabel Method: Excess Scaling. 2.1 Definitions CMSC 29700
CMSC 9700 Supervised Reading & Research Week 6: May 17, 013 Improvements on the Push-Relabel Method: Excess Scaling Rahul Mehta 1 Introduction We now know about both the methods based on the idea of Ford
More informationConnectivity-aware Virtual Network Embedding
Connectivity-aware Virtual Network Embedding Nashid Shahriar, Reaz Ahmed, Shihabur R. Chowdhury, Md Mashrur Alam Khan, Raouf Boutaba Jeebak Mitra, Feng Zeng Outline Survivability in Virtual Network Embedding
More informationRetiming. Adapted from: Synthesis and Optimization of Digital Circuits, G. De Micheli Stanford. Outline. Structural optimization methods. Retiming.
Retiming Adapted from: Synthesis and Optimization of Digital Circuits, G. De Micheli Stanford Outline Structural optimization methods. Retiming. Modeling. Retiming for minimum delay. Retiming for minimum
More informationNP-Hardness. We start by defining types of problem, and then move on to defining the polynomial-time reductions.
CS 787: Advanced Algorithms NP-Hardness Instructor: Dieter van Melkebeek We review the concept of polynomial-time reductions, define various classes of problems including NP-complete, and show that 3-SAT
More informationConstruction of Minimum-Weight Spanners Mikkel Sigurd Martin Zachariasen
Construction of Minimum-Weight Spanners Mikkel Sigurd Martin Zachariasen University of Copenhagen Outline Motivation and Background Minimum-Weight Spanner Problem Greedy Spanner Algorithm Exact Algorithm:
More informationCSE 417 Network Flows (pt 4) Min Cost Flows
CSE 417 Network Flows (pt 4) Min Cost Flows Reminders > HW6 is due Monday Review of last three lectures > Defined the maximum flow problem find the feasible flow of maximum value flow is feasible if it
More informationAn Initial Study of the Multi-Constraint Routing Problem Using Genetic Algorithm
An Initial Study of the Multi-Constraint Routing Problem Using Genetic Algorithm Zhongchao Yu Dept. of Computer Science University of Maryand College Park, MD 20742 yuzc@cs.umd.edu ABSTRACT Multi-constrained
More informationPrinciples of AI Planning. Principles of AI Planning. 7.1 How to obtain a heuristic. 7.2 Relaxed planning tasks. 7.1 How to obtain a heuristic
Principles of AI Planning June 8th, 2010 7. Planning as search: relaxed planning tasks Principles of AI Planning 7. Planning as search: relaxed planning tasks Malte Helmert and Bernhard Nebel 7.1 How to
More informationGreedy algorithms Or Do the right thing
Greedy algorithms Or Do the right thing March 1, 2005 1 Greedy Algorithm Basic idea: When solving a problem do locally the right thing. Problem: Usually does not work. VertexCover (Optimization Version)
More informationW[1]-hardness. Dániel Marx. Recent Advances in Parameterized Complexity Tel Aviv, Israel, December 3, 2017
1 W[1]-hardness Dániel Marx Recent Advances in Parameterized Complexity Tel Aviv, Israel, December 3, 2017 2 Lower bounds So far we have seen positive results: basic algorithmic techniques for fixed-parameter
More informationSteiner Trees and Forests
Massachusetts Institute of Technology Lecturer: Adriana Lopez 18.434: Seminar in Theoretical Computer Science March 7, 2006 Steiner Trees and Forests 1 Steiner Tree Problem Given an undirected graph G
More informationOverview of Constraint-Based Path Selection Algorithms for QoS Routing
Overview of Constraint-Based Path Selection Algorithms for QoS Routing F.A. Kuipers, Delft University of Technology T. Korkmaz, University of Texas at San Antonio M. Krunz, University of Arizona P. Van
More informationLEAST COST ROUTING ALGORITHM WITH THE STATE SPACE RELAXATION IN A CENTRALIZED NETWORK
VOL., NO., JUNE 08 ISSN 896608 00608 Asian Research Publishing Network (ARPN). All rights reserved. LEAST COST ROUTING ALGORITHM WITH THE STATE SPACE RELAXATION IN A CENTRALIZED NETWORK Y. J. Lee Department
More information3 No-Wait Job Shops with Variable Processing Times
3 No-Wait Job Shops with Variable Processing Times In this chapter we assume that, on top of the classical no-wait job shop setting, we are given a set of processing times for each operation. We may select
More informationFast Exact MultiConstraint Shortest Path Algorithms
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the ICC 27 proceedings. Fast Exact MultiConstraint Shortest Path Algorithms
More informationRobust validation of network designs under uncertain demands and failures
Robust validation of network designs under uncertain demands and failures Yiyang Chang, Sanjay Rao, and Mohit Tawarmalani Purdue University USENIX NSDI 2017 Validating network design Network design today
More informationPERFECT MATCHING THE CENTRALIZED DEPLOYMENT MOBILE SENSORS THE PROBLEM SECOND PART: WIRELESS NETWORKS 2.B. SENSOR NETWORKS OF MOBILE SENSORS
SECOND PART: WIRELESS NETWORKS 2.B. SENSOR NETWORKS THE CENTRALIZED DEPLOYMENT OF MOBILE SENSORS I.E. THE MINIMUM WEIGHT PERFECT MATCHING 1 2 ON BIPARTITE GRAPHS Prof. Tiziana Calamoneri Network Algorithms
More informationThe Size Robust Multiple Knapsack Problem
MASTER THESIS ICA-3251535 The Size Robust Multiple Knapsack Problem Branch and Price for the Separate and Combined Recovery Decomposition Model Author: D.D. Tönissen, Supervisors: dr. ir. J.M. van den
More informationFinding Critical Regions and Region-Disjoint Paths in a Network Term Paper
Finding Critical Regions and Term Paper Jean Olimb Department of Electrical & Computer Engineering Missouri University of Science and Technology SJOFX3@mst.edu, 23 February 2017 rev. 1.0 2017 solimb Outline
More informationLecture 4: Primal Dual Matching Algorithm and Non-Bipartite Matching. 1 Primal/Dual Algorithm for weighted matchings in Bipartite Graphs
CMPUT 675: Topics in Algorithms and Combinatorial Optimization (Fall 009) Lecture 4: Primal Dual Matching Algorithm and Non-Bipartite Matching Lecturer: Mohammad R. Salavatipour Date: Sept 15 and 17, 009
More informationTopic: Local Search: Max-Cut, Facility Location Date: 2/13/2007
CS880: Approximations Algorithms Scribe: Chi Man Liu Lecturer: Shuchi Chawla Topic: Local Search: Max-Cut, Facility Location Date: 2/3/2007 In previous lectures we saw how dynamic programming could be
More informationApproximation Algorithms: The Primal-Dual Method. My T. Thai
Approximation Algorithms: The Primal-Dual Method My T. Thai 1 Overview of the Primal-Dual Method Consider the following primal program, called P: min st n c j x j j=1 n a ij x j b i j=1 x j 0 Then the
More informationFast and Simple Algorithms for Weighted Perfect Matching
Fast and Simple Algorithms for Weighted Perfect Matching Mirjam Wattenhofer, Roger Wattenhofer {mirjam.wattenhofer,wattenhofer}@inf.ethz.ch, Department of Computer Science, ETH Zurich, Switzerland Abstract
More information15-854: Approximations Algorithms Lecturer: Anupam Gupta Topic: Direct Rounding of LP Relaxations Date: 10/31/2005 Scribe: Varun Gupta
15-854: Approximations Algorithms Lecturer: Anupam Gupta Topic: Direct Rounding of LP Relaxations Date: 10/31/2005 Scribe: Varun Gupta 15.1 Introduction In the last lecture we saw how to formulate optimization
More information/633 Introduction to Algorithms Lecturer: Michael Dinitz Topic: Approximation algorithms Date: 11/27/18
601.433/633 Introduction to Algorithms Lecturer: Michael Dinitz Topic: Approximation algorithms Date: 11/27/18 22.1 Introduction We spent the last two lectures proving that for certain problems, we can
More informationLecture 7: Asymmetric K-Center
Advanced Approximation Algorithms (CMU 18-854B, Spring 008) Lecture 7: Asymmetric K-Center February 5, 007 Lecturer: Anupam Gupta Scribe: Jeremiah Blocki In this lecture, we will consider the K-center
More information6 Randomized rounding of semidefinite programs
6 Randomized rounding of semidefinite programs We now turn to a new tool which gives substantially improved performance guarantees for some problems We now show how nonlinear programming relaxations can
More informationTaking Stock. IE170: Algorithms in Systems Engineering: Lecture 20. Example. Shortest Paths Definitions
Taking Stock IE170: Algorithms in Systems Engineering: Lecture 20 Jeff Linderoth Department of Industrial and Systems Engineering Lehigh University March 19, 2007 Last Time Minimum Spanning Trees Strongly
More informationThe Ordered Covering Problem
The Ordered Covering Problem Uriel Feige Yael Hitron November 8, 2016 Abstract We introduce the Ordered Covering (OC) problem. The input is a finite set of n elements X, a color function c : X {0, 1} and
More informationPERFECT MATCHING THE CENTRALIZED DEPLOYMENT MOBILE SENSORS THE PROBLEM SECOND PART: WIRELESS NETWORKS 2.B. SENSOR NETWORKS OF MOBILE SENSORS
SECOND PART: WIRELESS NETWORKS.B. SENSOR NETWORKS THE CENTRALIZED DEPLOYMENT OF MOBILE SENSORS I.E. THE MINIMUM WEIGHT PERFECT MATCHING ON BIPARTITE GRAPHS Prof. Tiziana Calamoneri Network Algorithms A.y.
More informationRepetition: Primal Dual for Set Cover
Repetition: Primal Dual for Set Cover Primal Relaxation: k min i=1 w ix i s.t. u U i:u S i x i 1 i {1,..., k} x i 0 Dual Formulation: max u U y u s.t. i {1,..., k} u:u S i y u w i y u 0 Harald Räcke 428
More informationα Coverage to Extend Network Lifetime on Wireless Sensor Networks
Noname manuscript No. (will be inserted by the editor) α Coverage to Extend Network Lifetime on Wireless Sensor Networks Monica Gentili Andrea Raiconi Received: date / Accepted: date Abstract An important
More informationSimple Quality-of-Service Path First Protocol and Modeling Analysis*
Simple Quality-of-Service Path First Protocol and Modeling Analysis* Lin Shen, Mingwei Xu, Ke Xu, Yong Cui, Youjian Zhao Department of Computer Science, Tsinghua University, Beijing, P.R.China, 100084
More informationOptimal Topology Design for Overlay Networks
Optimal Topology Design for Overlay Networks Mina Kamel 1, Caterina Scoglio 1, and Todd Easton 2 1 Electrical and computer Engineering Department 2 Industrial and Manufacturing Systems Engineering Department
More informationIntroduction to Approximation Algorithms
Introduction to Approximation Algorithms Dr. Gautam K. Das Departmet of Mathematics Indian Institute of Technology Guwahati, India gkd@iitg.ernet.in February 19, 2016 Outline of the lecture Background
More informationAn O(log n/ log log n)-approximation Algorithm for the Asymmetric Traveling Salesman Problem
An O(log n/ log log n)-approximation Algorithm for the Asymmetric Traveling Salesman Problem and more recent developments CATS @ UMD April 22, 2016 The Asymmetric Traveling Salesman Problem (ATSP) Problem
More informationAlgorithm Design and Analysis
Algorithm Design and Analysis LECTURE 29 Approximation Algorithms Load Balancing Weighted Vertex Cover Reminder: Fill out SRTEs online Don t forget to click submit Sofya Raskhodnikova 12/7/2016 Approximation
More informationCS599: Convex and Combinatorial Optimization Fall 2013 Lecture 14: Combinatorial Problems as Linear Programs I. Instructor: Shaddin Dughmi
CS599: Convex and Combinatorial Optimization Fall 2013 Lecture 14: Combinatorial Problems as Linear Programs I Instructor: Shaddin Dughmi Announcements Posted solutions to HW1 Today: Combinatorial problems
More informationCommunication Networks I December 4, 2001 Agenda Graph theory notation Trees Shortest path algorithms Distributed, asynchronous algorithms Page 1
Communication Networks I December, Agenda Graph theory notation Trees Shortest path algorithms Distributed, asynchronous algorithms Page Communication Networks I December, Notation G = (V,E) denotes a
More informationOPTICAL NETWORKS. Virtual Topology Design. A. Gençata İTÜ, Dept. Computer Engineering 2005
OPTICAL NETWORKS Virtual Topology Design A. Gençata İTÜ, Dept. Computer Engineering 2005 Virtual Topology A lightpath provides single-hop communication between any two nodes, which could be far apart in
More informationSolutions for the Exam 6 January 2014
Mastermath and LNMB Course: Discrete Optimization Solutions for the Exam 6 January 2014 Utrecht University, Educatorium, 13:30 16:30 The examination lasts 3 hours. Grading will be done before January 20,
More informationBasic Approximation algorithms
Approximation slides Basic Approximation algorithms Guy Kortsarz Approximation slides 2 A ρ approximation algorithm for problems that we can not solve exactly Given an NP-hard question finding the optimum
More informationOn the Robustness of Distributed Computing Networks
1 On the Robustness of Distributed Computing Networks Jianan Zhang, Hyang-Won Lee, and Eytan Modiano Lab for Information and Decision Systems, Massachusetts Institute of Technology, USA Dept. of Software,
More informationRandomized rounding of semidefinite programs and primal-dual method for integer linear programming. Reza Moosavi Dr. Saeedeh Parsaeefard Dec.
Randomized rounding of semidefinite programs and primal-dual method for integer linear programming Dr. Saeedeh Parsaeefard 1 2 3 4 Semidefinite Programming () 1 Integer Programming integer programming
More informationW[1]-hardness. Dániel Marx 1. Hungarian Academy of Sciences (MTA SZTAKI) Budapest, Hungary
W[1]-hardness Dániel Marx 1 1 Institute for Computer Science and Control, Hungarian Academy of Sciences (MTA SZTAKI) Budapest, Hungary School on Parameterized Algorithms and Complexity Będlewo, Poland
More informationDesigning robust network topologies for wireless sensor networks in adversarial environments
Designing robust network topologies for wireless sensor networks in adversarial environments Aron Laszka a, Levente Buttyán a, Dávid Szeszlér b a Department of Telecommunications, Budapest University of
More informationOn the Robustness of Distributed Computing Networks
1 On the Robustness of Distributed Computing Networks Jianan Zhang, Hyang-Won Lee, and Eytan Modiano Lab for Information and Decision Systems, Massachusetts Institute of Technology, USA Dept. of Software,
More informationOn the Min-Max 2-Cluster Editing Problem
JOURNAL OF INFORMATION SCIENCE AND ENGINEERING 29, 1109-1120 (2013) On the Min-Max 2-Cluster Editing Problem LI-HSUAN CHEN 1, MAW-SHANG CHANG 2, CHUN-CHIEH WANG 1 AND BANG YE WU 1,* 1 Department of Computer
More informationLecture 6: Linear Programming for Sparsest Cut
Lecture 6: Linear Programming for Sparsest Cut Sparsest Cut and SOS The SOS hierarchy captures the algorithms for sparsest cut, but they were discovered directly without thinking about SOS (and this is
More information2386 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 52, NO. 6, JUNE 2006
2386 IEEE TRANSACTIONS ON INFORMATION THEORY, VOL. 52, NO. 6, JUNE 2006 The Encoding Complexity of Network Coding Michael Langberg, Member, IEEE, Alexander Sprintson, Member, IEEE, and Jehoshua Bruck,
More informationOutline: Finish uncapacitated simplex method Negative cost cycle algorithm The max-flow problem Max-flow min-cut theorem
Outline: Finish uncapacitated simplex method Negative cost cycle algorithm The max-flow problem Max-flow min-cut theorem Uncapacitated Networks: Basic primal and dual solutions Flow conservation constraints
More informationUNIVERSITY OF TORONTO Department of Computer Science April 2014 Final Exam CSC373H1S Robert Robere Duration - 3 hours No Aids Allowed.
UNIVERSITY OF TORONTO Department of Computer Science April 2014 Final Exam CSC373H1S Robert Robere Duration - 3 hours No Aids Allowed. PLEASE COMPLETE THE SECTION BELOW AND THE SECTION BEHIND THIS PAGE:
More informationUnicast and Multicast QoS Routing with Multiple Constraints
481 Unicast and Multicast QoS Routing with Multiple Constraints Dan Wang 1, Funda Ergun 1,andZhanXu 2 1 School of Computer Science, Simon Fraser University, Burnaby BC V5A 1S6, Canada {danw,funda}@cs.sfu.ca
More informationIEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 3, MARCH
IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 15, NO. 3, MARCH 2016 1907 Joint Flow Routing and DoF Allocation in Multihop MIMO Networks Xiaoqi Qin, Student Member, IEEE, Xu Yuan, Student Member,
More information11. APPROXIMATION ALGORITHMS
11. APPROXIMATION ALGORITHMS load balancing center selection pricing method: vertex cover LP rounding: vertex cover generalized load balancing knapsack problem Lecture slides by Kevin Wayne Copyright 2005
More informationAlgorithms for Integer Programming
Algorithms for Integer Programming Laura Galli November 9, 2016 Unlike linear programming problems, integer programming problems are very difficult to solve. In fact, no efficient general algorithm is
More information