Cooperative Data Dissemination to Mission Sites

Transcription

1 Cooperative Data Dissemination to Mission Sites Fangfei Chen a, Matthew P. Johnson b, Amotz Bar-Noy b and Thomas F. La Porta a a Department of Computer Science and Engineering, the Pennsylvania State University b Department of Computer Science, the City University of New York Graduate Center ABSTRACT Timely dissemination of information to mobile users is vital in many applications. In a critical situation, no network infrastructure may be available for use in dissemination, over and above the on-board storage capability of the mobile users themselves. We consider the following specialized content distribution application: a group of users equipped with wireless devices build an ad hoc network in order cooperatively to retrieve information from certain regions (the mission sites). Each user requires access to some set of information items originating from sources lying within a region. Each user desires low-latency access to its desired data items, upon request (i.e., when pulled). In order to minimize average response time, we allow users to pull data either directly from sources or, when possible, from other nearby users who have already pulled, and continue to carry, the desired data items. That is, we allow for data to be pushed to one user and then pulled by one or more additional users. The total latency experienced by a user vis-vis a certain data item is then in general a combination of the push delay and the pull delay. We assume each delay time is a function of the hop distance between the pair of points in question. Our goal in this paper is to assign data to mobile users, in order to minimize the total cost and the average latency experienced by all the users. In a static setting, we solve this problem in two different schemes, one of which is easy to solve but wasteful, one of which relates to NP-hard problems but is less so. Then in a dynamic setting, we adapt the algorithm for the static setting and develop a new algorithm with respect to users gradual arrival. In the end we show a trade-off can be made between minimizing the cost and latency. Introduction Timely dissemination of information to mobile users is vital in many applications. In a critical situation, no network infrastructure may be available for use in dissemination, over and above the on-board storage capability of the mobile users themselves. We consider the following specialized content distribution application: a group of users equipped with wireless devices build an ad hoc network in order cooperatively to retrieve information from certain regions (the mission sites). Each user requires access to some set of information items originating from sources lying throughout a region. Each user desires low-latency access to its desired data items, upon request (i.e., when pulled). In order to minimize average response time, we allow users to pull data either directly from sources or, when possible, from other nearby users who have already pulled, and continue to carry, the desired data items. That is, we allow for data to be pushed to one user and then pulled by one or more additional users. In previous work, for a similar scenario, data is pushed to some storage nodes at the mission site where it may be retrieved locally when users arrive. The goal is to choose a storage node assignment minimizing the total latency-based cost. Since the number and storage capacity of storage nodes are both limited, the problem is proved to be NP-hard even to approximate. In this work, we assume no network infrastructure is available for assistance, that is, the group of users need to build an ad hoc network and cooperatively retrieve information by themselves. We start with a static problem setting in which all users already arrive when the dissemination starts. Users not within the communication range of each other can communicate by multi-hop routing protocols. Assuming the network is connected, data can be delivered to any of the users. Our goal in this setting is to minimize the total number of hops it takes to disseminate every data to the requesting users. We assume each user has enough space to contribute in the dissemination, which makes a simple sharing scheme, One-to-Many, solvable in polynomial time. However, when we try to further reduce the cost through a more complicated sharing scheme, computing the costs involves solving NP-hard problems. We provide a heuristic approximation algorithm for this setting and compare its performance, through simulation, with the One-to-Many Scheme s.

2 Then we introduce the dynamic setting, that is, users gradually arrive after the dissemination begins. Besides the number of hops, we take user-experienced latency into consideration. That is, the time between when users arrive and when they receive the first piece of their data. Since we have no dedicated storage nodes, data can be retrieved only from users that have already arrived. Another complication is that the network may not be fully connected until a certain point. Therefore, always trying to minimize the number of hops as in the static setting may increase the average latency. We adapt our algorithm for this dynamic setting as a base-level comparison and propose a new greedy algorithm. Finally, we demonstrate a trade-off between minimizing the number of hops and the average latency. The rest of this paper is organized as follows. Section presents related work. Section formulates the problem in static settings and propose two schemes for solving the problem. Section shows how we generate simulations and evaluate the algorithms. Section 5 discusses challenges encountered when solving the problem in the dynamic setting and proposes a new algorithm. Section 6 concludes the paper. Related Work Our efforts here relate to a body of work on Peer-to-Peer Content Distribution (PP CDN). Such a system, according to the survey of Androutsellis-Theotokis and Spinellis, creates a distributed storage medium that allows for the publishing, searching, and retrieval of files by members of its network. Unlike a traditional CDN, a PP Content Distribution Network requires very few or even no network infrastructure and is therefore scalable and easy to deploy. Our model differs from PP CDNs, however, in that the information needs for each user are predefined. PP CDNs are designed to provide users access to all available files, in which case files are stored and indexed that may not be requested over long periods of time. We are motivated by critical situations in which all available bandwidth must be taken advantage of in order to serve as many user demands as possible. Therefore we store and deliver only data for which there is need. Another more technical difference is that each data item in our problem is treated as an unsplittable whole, different copies of which appear for different users, while in PP CDNs data is normally broken into parts and stored in a distributed way. Another important aspect of our work is that each data item can be requested by multiple users, which relates the problem to the study of multicast protocols. The benefit of multicast over using traditional multiple unicast links is that the source only needs to do a single transmission of the data, which will then be propagated by the network. Analogously, in our work sources send data items to one user, who then makes the item available to other users who in turn may share it further. One specific scenario we study is one in which users gradually arrive; one of our considerations in evaluating solutions is user-experienced latency. This paper is a direct extension of our previous work, in which data is pushed to storage nodes at the mission site where it may be retrieved locally when users arrive. The storage space on each nearby node is limited, yielding a variant of the Multiple Knapsack Problem in which our goal is to choose a storage node assignment minimizing the total latency-based cost. We used a simple One-to-Many Scheme, under which all users need to retrieve data from the storage nodes. In this new work, we attempt to improve the one-to-many dissemination structure by introducing a spanning tree structure or even a dynamically growing structure. Each data item, newly delivered to its first user, presents an instance of the Steiner Tree problem, which is a classical NP-hard problem 5 originally posed by Gauss. That problem is known to admit a.55-approximation, 6 but a simple -approximation algorithm 7 based on spanning trees is well known, which we adapt here as a heuristic algorithm. In the previous work we used a static network topology, assuming storages nodes were deployed ahead of time, with fixed locations, so users experienced latency could vary depending on whether the data was ready at the storage node at the time of users arrival. In the current paper, however, the latency varies mainly because of changes to network topology over time. Evaluating different strategies to deal with this latency, we show that a trade-off can be achieved between latency and cost. Static Settings We start with problem settings in which all mobile users have already arrived at the mission site when the dissemination begins. In this section, we formally define the problem and discuss two solution schemes, which we evaluate through simulation later in the paper.

3 . Problem definition Let D = {d i : i =... m} be a set of data items and U = {u j : j =... n} be a set of users. Each data item d i has a size s i and is co-located with one of the users (we need at least one user who can reach the data item in only one hop). Each user must retrieve some subset D j D of the data items. Unlike in the previous work, we assume each user has enough storage space for both storing its own items and passing on others items. Each potential placement of d i in u j (u j does not necessarily request d j ) is associated with some cost c ij. The objective is to minimize the cost of dissemination of all data items. The problem is formally defined as: min i,j c ij x ij () s.t. j x ij = i x ij {0, } i, j Hop count is a natural metric for cost of delivering data in wireless networks. In previous work, we used distance as a proxy of hop count. In this work, we more accurately use the exact number of hops based on the shortest path routing. It is crucial to note that different dissemination schemes will result in different cost values c ij, and indeed computing the true values of these costs may not be easy.. One-to-Many Scheme A naive approach to solve this new problem is to directly apply the previous algorithm (for the problem setting in which items are assigned to one storage node and then pulled by users interested). We call it One-to- Many scheme (see Figure (a)). In this scheme, one user stores the data item and then other users who request the data item retrieve it only from this first user. In this way, the user simulates the functionality of a storage node in the previous work. The cost c ij of placing data item j in user i is based on the total cost for all other users desiring item j to access it direct from user i. Let U i denote the subset of users requesting data item i, (a) One-to-Many Scheme. (b) Spanning Tree Scheme. Figure : Two Schemes. and let h xy be the minimum number of hops from u x to u y. Then the cost to store data i on user j is: c ij = s i (h ij + ) () k:u k U i h jk Furthermore, we may consider the user who has direct access to d i as another user requesting d i, then we may remove the push part from the calculation: c ij = s i h jk () k:u k U i

4 h xy can be obtained by Dijkstra s algorithm in polynomial time. Since there is no capacity constraint on the users, the optimal placement decisions for the data items can all be made independently, by enumeration in polynomial time. Given the specified cost values c ij, the One-to-Many Scheme (see Algorithm ), chooses the best placement for each item. Algorithm One-to-Many Scheme : for i = to m do : for j = to n do : c ij s i k:u k U i h jk : end for 5: j argmin c ij j 6: assign d i to u j 7: end for. Spanning Tree Scheme Although the One-to-Many Scheme is very simple, it likely introduces a lot of redundant traffic between the user who stores the data and other users. A more sophisticated approach is to use an algorithm that takes advantage of all the freedom this new problem setting affords (i.e., allowing each user to pass the item to the next). Since data only needs to reach each recipient once, what is desired for each data item is a tree structure rooted at the first recipient and including all the other recipients as nodes (see Figure (b)). The nodes of a given data item s tree need not be limited to users desiring that item, however, since we allow users to carry items that they do not themselves need, in order to provide aid users. The tree for each data item therefore is required to contain nodes for all that item s users, the node who has direct access to it and it may optionally include nodes for other users as well. The cost of a tree is the sum of its edge-weights. Finding the lowest-cost such tree is an instance of the Steiner tree 5 problem: given a graph G = (V, E) and a subset S V, find a minimum-cost connected subgraph of G that spans all vertices of S. Although the Steiner Tree problem is NP-hard in general, it admits a.55-approximation algorithm. 6 There is also a well known factor -approximation algorithm (discovered by many authors; see Vazirani 7 ) that begins by computing a minimum spanning tree (MST) on the graph induced by the required nodes S. We opt to use a variation on the MST-based algorithm which, while sacrificing the approximation guarantee, has practical advantages in efficiency. We compute a spanning tree out of G for each user j and construct it as being rooted at j. For each item i that we consider placing in user j, we prune any redundant leaves from the tree rooted at j, i.e., users who do not desire item j and are not needed to forward it to others. User j can then forward any data items it possesses to users desiring them, along the paths of this tree. We use Algorithm to calculate Algorithm Tree Scheme calculation of c ij values : T = T (V, E) is the MST rooted at u j : V V, E E : sort vertices V in level order in T : for k = n down to do 5: if v k is a leaf node and u k / U i then 6: remove v k from V 7: remove all edges of v k from E 8: end if 9: c ij s i E 0: end for the actual number of hops implied by the pruned spanning tree. Given the computed c ij values, we again use Algorithm (except with the new computation of c ij replacing line ) to choose the best assignment for each item. As assignment is now understood to mean that item i will be disseminated from the pruned spanning tree rooted at user j.

5 Evaluation In this section, we evaluate the two algorithms under different circumstances. First we present the evaluation settings and explain how we generate random problem instances. Then we explain the results and compare the algorithms.. Problem instance generation We use undirected graphs to model the network of communication between users. For each set of parameters we test, we first need to generate a random graph representing the problem instance. We require that the graph is connected so that there is a route from any user to any other user in the network. For this, we use a modified version of the Barabasi and Albert scale-free network model 8 (see Algorithm ). In the original paper, 8 the Algorithm Random Connected Graph Generation : G = {V, E} = : for j = to n do : V V v j, nedges = 0 : for i = to j do 5: r random() 6: prob C deg(v i )/ E 7: if r prob then 8: E E {(v i, v j )} 9: nedges nedges + 0: end if : end for : if nedges = 0 then : v j has the largest deg(v j ) : E E {(v i, v j )} 5: end if 6: end for probability p of creating an edge between an existing vertex v and the newly added vertex is: p = deg(v)/ E Here deg(v) indicates the degree of vertex v, i.e., the number of users v can directly communicate with. We multiply this probability by a factor of C (the vertex degree parameter), in order to adjust the number of edges in the graph. Each time we add a new vertex, we check the number of edges we add connecting to this vertex. If no edge is added, we simply connect the new vertex to the vertex with the largest degree so that the graph remains connected after each step. The sizes of data items are selected uniformly at random from [, maxdatasize]. Assuming at least one user can read each data item directly, each data item is randomly assigned to one of the users as sources. Each data item is requested by a given user with probability reqp rob. By default, we set the number of data items to 50, the number of users to 50, reqp rob = 0., C = and maxdatasize = 0. To test the performance of the algorithms, we count the total number of hops in four separate series of simulations, each varying one of the following parameters: the number of the data items, the number of users, reqp rob and C.. Results The Spanning Tree scheme constantly beats the One-to-Many Scheme in these four tests (see Figure ), although their divergence is not unbounded. When we expand the problem instance size, by increasing either the number of data items or the number of users, we consistently find One-to-Many Scheme s hop count to be within a constant factor of Spanning Tree s (see Figures (a) and (b)).

6 8 x 0 7 One to Many Scheme Spanning Tree Scheme x 0 One to Many Scheme Spanning Tree Scheme 6 0 Number of hops 5 Number of hops Number of data items (a) The number of data items Number of users (b) The number of users. 8 x 0 7 One to Many Scheme Spanning Tree Scheme.5 x 05. One to Many Scheme Spanning Tree Scheme 6.5 Number of hops 5 Number of hops User request rate (c) The user request rate Vertex degree parameter (d) The vertex degree parameter. Figure : Evaluation results, varying the specified parameter. In the third test, we fix the numbers of data items and users while varying the user request probability reqp rob. As we increase reqp rob, each data item is requested by more and more users. In Figure (c), we see that the number of hops by the One-to-Many Scheme increases linearly, because each additional request will result in a new path from the root that stores the data. The hop count of the Spanning Tree Scheme tends to grow sublinearly, because we typically only need to extend the existing tree structure modestly for each additional request. In the fourth test, we increase the probability with which a new vertex connects to existing nodes during the random graph generation. As the probability increases average degree, so the depth of the graph decreases. Therefore, we expect the number of hops to decrease for both the two schemes, which is indeed what we observe (see Figure (d)). 5 Dynamic Settings In this section, we start to look at the case in which users arrive gradually after the dissemination begins. First, we adapt our algorithms for the static case to this new setting. Then we propose a greedy algorithm which takes into consideration the user-experienced latency. We again run simulations to compare these algorithms. Since users arrive at different moments in this dynamic setting, they may experience highly variable retrieval latency even for the same data item. Because the network connectivity changes over time, some users may even be unreachable until a certain point. As a result, the time users spend waiting for connecting to the network may be much longer than the actual transmission latency. We define user-experienced latency to be the time between a user s arrival and the moment when it receives the first part of the data item.

7 5. Spanning Tree The Spanning Tree Scheme focuses on minimizing the total number of hops; it takes no consideration of the users arrival time. Moreover, it assumes the current presence of all nodes. Nonetheless, we can apply it here by ) assuming a priori knowledge of nodes that will eventually arrive, and ) disseminating via the spanning tree and caching data as needed until each next-hop node arrives. Once the nodes arrive, we can continue with the dissemination immediately. When a user arrives, however, he may have to wait until all his ancestor nodes in the spanning tree have also arrived. 5. Greedy A trade-off can be made if we allow the dissemination not to follow the spanning tree. Then, as soon as a user becomes reachable from other users, we can deliver all its requested data items following the current shortest paths, which may be different from the shortest paths in the full graph. We call this the Greedy algorithm (see Algorithm ). Algorithm Greedy algorithm : for each new user arrival do : update the connectivity graph G : for each user j that becomes newly reachable do : for each data item i that user j requests do 5: find the nearest user k that has data i in G 6: deliver data i from user k to user j 7: end for 8: end for 9: end for 5. Evaluation We compare the two algorithms in terms of the total number of hops and the sum of users experienced latency. For simplicity, we assume that one unit size data needs one time slot to do one hop transmission. We conduct simulations similar to those in Section, except that we record the user-experienced latency as well. 8 x 05 7 Greedy Spanning Tree.5 x 05 Greedy Spanning Tree Total experienced delay 6 5 Total number of hops Number of Data Items (a) Total experienced delay Number of Data Items (b) Total number of hops. Figure : Trials varying the number of data items. In the first set of experiments, we vary the number of data items. In Figure (a), we can see that the Greedy algorithm always results in lower latency than the Spanning Tree algorithm. In Figure (b), we see that the spanning tree always beats the Greedy algorithm in terms of number of hops. This is what we expected based on the focuses of the two algorithms. In the second set of experiments, we increase the vertex degree factor. For the Greedy algorithm (see Figures (a) and (b)), we see both delay and number of hops decreasing quickly, because increasing the degree of

8 .5 x 05 Greedy Spanning Tree.7 x 05.6 Greedy Spanning Tree Total experienced delay.5.5 Total number of hops Vertex degree factor (a) Total experienced delay. Figure : Trials varying the vertex degree factor Vertex degree factor (b) Total number of hops. each node will both help the graph become connected sooner tend to decrease path lengths. The delay for the Spanning Tree algorithm, however, hardly decreases. Although nodes become connected to the graph sooner, since we force them to follow the spanning tree, the experienced latency is mostly determined by the parent node who arrives the last. The number of hops decreases as also happened in the former experiments. 6 Conclusion In this paper, we have studied a scenario in which users build an ad-hoc network to cooperatively disseminate data without relying on any network infrastructure. We start with a scenario in which all users arrive before the dissemination begins. Then we adopt our prior algorithms and propose a new algorithm for the case in which users arrive gradually over time. We evaluate these algorithms under different circumstances and show that a trade-off can be made between the total number of hops and the user-experienced latencies. ACKNOWLEDGMENTS Research was sponsored by US Army Research laboratory and the UK Ministry of Defence and was accomplished under Agreement Number W9NF The views and conclusions contained in this document are those of the authors and should not be interpreted as representing the official policies, either expressed or implied, of the US Army Research Laboratory, the U.S. Government, the UK Ministry of Defense, or the UK Government. The US and UK Governments are authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation hereon. REFERENCES. F. Chen, M. P. Johnson, A. Bar-Noy, I. Fermin, and T. La Porta, Proactive data dissemination to mission sites, 6th Annual IEEE Communications Society Conference on Sensor, Mesh and Ad Hoc Communications and Networks, June S. Androutsellis-Theotokis and D. Spinellis, A survey of peer-to-peer content distribution technologies, ACM Computing Surveys (CSUR) 6(), p. 7, 00.. S. Deering and D. Cheriton, Multicast routing in datagram internetworks and extended LANs, ACM Transactions on Computer Systems (TOCS) 8(), pp. 85 0, H. Kellerer, U. Pferschy, and D. Pisinger, Knapsack Problems, Springer, M. Garey and D. Johnson, Computers and Intractability: A Guide to the Theory of NP-Colmpleteness, Freeman, G. Robins and A. Zelikovsky, Tighter bounds for graph steiner tree approximation, SIAM J. Discrete Math. 9(), pp., V. V. Vazirani, Approximation Algorithms, Springer, A. Barabasi and R. Albert, Emergence of scaling in random networks, Science 86(59), p. 509, 999.