Data Communication. Guaranteed Delivery Based on Memorization

Transcription

1 Data Communication Guaranteed Delivery Based on Memorization

2 Motivation Many greedy routing schemes perform well in dense networks Greedy routing has a small communication overhead Desirable to run Greedy routing as long as possible However, greedy routing might fail in sparse networks Guaranteed delivery is desirable property as well On the following slides: in case of failure run a recovery mechanism which requires memorizing past routing information In the message In the visited node

3 Recovery by Flooding Stojmenovic, Lin: Partial flooding to guarantee delivery (f- GEDIR, f-mfr, f-dir) Intermediate nodes handle packet according to GEDIR, MFR, Concave node broadcasts packet to all neighbors To avoid message loops: concave node rejects further copies of the message, concave nodes are removed from the list of candidate nodes Example: Message from S to D B C A S E G F H D unicast broadcast

4 Recovery by Flooding When there is a path from source to destination then one of the neighbors lies on the path guaranteed delivery Observation: flooding produces many redundant message transmissions Improvement: Component routing Connected components in node v partitions in the one-hop neighborhood graph N(v) when removing v Algorithm Concave node determines connected components Forward message to only the best neighbor in each component Number of message transmissions reduced significantly e.g. concave node has at most four connected components in the unit disk graph model

5 DFS-Based Routing Jain et al.: Geographic Routing Algorithm (GRA) Intermediate node handles message greedily Concave node maintains route to destination node Start route discovery for outdated routing tables Stuck packet is routed to destination after successful route discovery How to perform route discovery?

6 DFS-Based Routing Depth first search from concave node S Yields an acyclic path from S to D Node X puts its address on route discovery packet p Forward to neighbor who has not seen p before Select neighbor Y which minimizes XY + YD If no possible neighbor exists, remove address from p and send it back to the node from which p was originally received Alternative implementation: memorize DFS data in nodes Other metrics may be applied on next neighbor selection Quality-of-service paths (delay and bandwidth criteria, connection time, ) t1, t6: path = W W root t2: path = W X X Y3 t5: path = W X Y3 Y2 t4: path = W X Y2 t3: path = W X Y1 Y1

7 Data Communication Memoryless Guaranteed Delivery

8 Motivation Disadvantage of greedy recovery based on memorizing traffic Traffic may increase Memorized data may be outdated Greedy routing does not suffer from this fact Instantaneous forwarding decision Not affected by previous (and probably outdated) state information Question: is there a recovery strategy which preserves greedy s memoryless property?

9 The Face Recovery Principle S D F1 C F2 F3 F4 F5 T A B Locally construct a planar graph Visit face sequence providing progress towards T Traverse faces according to the left/right hand rule Return into greedy mode whenever possible

10 Face Recovery Details When to change current face traversal? How to decide the next face locally?

11 Example 1 Greedy-Face-Greedy GFG, [Bose et al., 1999]

12 GFG The face routing part P S T F P S repeat Let F be the face with P on boundary and intersecting PT Traverse * F until reaching an edge that intersects PT at some point Q P P Q until P=T * counterclockwise if inner, clockwise if outer face

13 GFG The face routing part P Q S T F P S repeat Let F be the face with P on boundary and intersecting PT Traverse * F until reaching an edge that intersects PT at some point Q P P Q until P=T * counterclockwise if inner, clockwise if outer face

14 GFG The face routing part P S T F P S repeat Let F be the face with P on boundary and intersecting PT Traverse * F until reaching an edge that intersects PT at some point Q P P Q until P=T * counterclockwise if inner, clockwise if outer face

15 GFG The face routing part P S T F P S repeat Let F be the face with P on boundary and intersecting PT Traverse * F until reaching an edge that intersects PT at some point Q P P Q until P=T * counterclockwise if inner, clockwise if outer face

16 Example 2 Greedy Other Adaptive Face Routing GOAFR, [Kuhn et al., 2003]

17 Face Routing Part of GOAFR P S T F P S repeat Explore the complete boundary of face F containing the line PT Advance to Q on F s boundary which is closest to T and set P Q until reaching T

18 Face Routing Part of GOAFR P Q S T F P S repeat Explore the complete boundary of face F containing the line PT Advance to Q on F s boundary which is closest to T and set P Q until reaching T

19 Face Routing Part of GOAFR P Q S F T P S repeat Explore the complete boundary of face F containing the line PT Advance to Q on F s boundary which is closest to T and set P Q until reaching T

20 Face Routing Part of GOAFR F S T P S repeat Explore the complete boundary of face F containing the line PT Advance to Q on F s boundary which is closest to T and set P Q until reaching T Q P

21 General Face Change Mechanism Observation: face can be traversed in two directions V S T U W After crossing variant: U selects V Before crossing variant: U selects W Best angle variant: U selects W

22 Comparison of Variants

23 FACE over Dominating Set Fact: localized planar graph construction prefers short edges over long ones Affects performance of face traversal: increased hop count How to reduce number of network nodes used by FACE? Remember: connected dominating set subset S of nodes of a graph G which satisfies Induced subgraph G[S] is connected Each node in G is either in S or has a one-hop neighbor in S Datta et al.: Perform FACE algorithm only on internal nodes defined by a connected dominating set Gabriel graph construction performed on DS only If concave node is no internal node forward to neighbor in DS Route along Gabriel graph until Local minimum handled Or node with destination in its neighbor list reached

24 Shortcut-Based FACE Routing Possibly more neighbor nodes along path produced by face traversal Locally construct planar graph used by all neighbor nodes 2-hop neighbor information needed! Perform a local planar graph traversal until reaching the last node in view and send packet to that node directly D S

25 Geographical Cluster Based Routing

26 The main Idea u C S v F1 F2 F3 T w D Connect neighboring clusters connected by a pair of nodes No UDG assumption; nodes need to be connected within one cluster Message loosely follows faces of the planar overlay graph Graph exploration requires local knowledge of all adjacent clusters Forwarding requires connectivity within Cluster C

27 GCR versus FACE

28 GCR Enables Local Traffic Dispersion v A B C

29 The Impact of Mobility Destination Node Destination Cluster Source Node Source Cluster Routing on sub graph Routing on overlay

30 Performance Study on Success Rate

31 The Advantages of Overlays No geometric network requirements Cluster membership sufficient Greedy forwarding even in recovery mode More robust to mobility

32 The Bad News Disconnection S u v T

33 The Bad News Disconnection Consider all edges A C B

34 The Bad News Disconnection Consider all edges Not implicitly planar A C D B

35 The Bad News Disconnection Consider all edges Not implicitly planar Remove bad edges Always possible? Local detection?

36 Planarity and Connectivity

37 Planarization by Edge Removal Undirected graph Unit disk graph Circular transmission range Unique sending radius ( v, w) E vw R Aggregated UDG? (a) A B C D Observation Redundancy Property Locally detectable intersection (b) D B Planarity and connectivity? C A

38 Redundancy Property not Sufficient Assumption Arbitrary network Redundancy property u1 u2 Conflicting goals Planarity Connectivity u5 v4 v3 v5 w v2 v1 u3 Additional property? ( co-existence property) u4

39 Aggregated Gabriel Graph Construction Properties

40 Aggregated Gabriel Graph Construction Gabriel graph on UDG Properties u v w

41 Aggregated Gabriel Graph Construction Gabriel graph on UDG Aggregation afterwards Properties

42 Aggregated Gabriel Graph Construction Gabriel graph on UDG Aggregation afterwards Properties Connected No regular intersection Localized construction Planar?

43 Irregular Intersection Problem Aggregated Graph A u v B w C Sub Graph 1 A u v B w C Sub graph 2 A u v B w C

44 Purged Aggregated Gabriel Graph Irregular intersection ABxC A C B

45 Purged Aggregated Gabriel Graph Irregular intersection ABxC UDG exists AC or BC A C B

46 Purged Aggregated Gabriel Graph Irregular intersection ABxC UDG exists AC or BC A Remove AB C B

47 Purged Aggregated Gabriel Graph Irregular intersection ABxC UDG exists AC or BC A Remove AB Introduce implicit edge BC Properties Planar Connected Localized construction possible Forwarding along implicit edge BC? C B