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24
Network Coding for Large Scale Content Distribution
"... We propose a new scheme for content distribution of large files that is based on network coding. With network coding, each node of the distribution network is able to generate and transmit encoded blocks of information. The randomization introduced by the coding process eases the scheduling of bloc ..."
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Cited by 361 (6 self)
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We propose a new scheme for content distribution of large files that is based on network coding. With network coding, each node of the distribution network is able to generate and transmit encoded blocks of information. The randomization introduced by the coding process eases the scheduling of block propagation, and, thus, makes the distribution more efficient. This is particularly important in large unstructured overlay networks, where the nodes need to make decisions based on local information only. We compare network coding to other schemes that transmit unencoded information (i.e. blocks of the original file) and, also, to schemes in which only the source is allowed to generate and transmit encoded packets. We study the performance of network coding in heterogeneous networks with dynamic node arrival and departure patterns, clustered topologies, and when incentive mechanisms to discourage freeriding are in place. We demonstrate through simulations of scenarios of practical interest that the expected file download time improves by more than 2030 % with network coding compared to coding at the server only and, by more than 23 times compared to sending unencoded information. Moreover, we show that network coding improves the robustness of the system and is able to smoothly handle extreme situations where the server and nodes departure the system.
Network Coding in Undirected Networks
, 2004
"... Recent work in network coding shows that, it is necessary to consider both the routing and coding strategies to achieve optimal throughput of information transmission in data networks. So far, most research on network coding has focused on the model of directed networks, where each communication li ..."
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Cited by 69 (14 self)
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Recent work in network coding shows that, it is necessary to consider both the routing and coding strategies to achieve optimal throughput of information transmission in data networks. So far, most research on network coding has focused on the model of directed networks, where each communication link has a fixed direction. In this paper, we study the benefits of network coding in undirected networks, where each communication link is bidirectional. Our theoretical results show that, for a single unicast or broadcast session, there are no improvements with respect to throughput due to network coding. In the case of a single multicast session, such an improvement is bounded by a factor of two, as long as half integer routing is permitted. This is dramatically different from previous results obtained in directed networks. We also show that multicast throughput in an undirected network is independent of the selection of the sender within the multicast group. We finally show that, rather than improving the optimal achievable throughput, the benefit of network coding is to significantly facilitate the design of efficient algorithms to compute and achieve such optimal throughput. I.
Approximation Hardness of the Steiner Tree Problem on Graphs
 Proceedings of the 8th Scandinavian Workshop on Algorithm Theory, SWAT 2002, Springer, LNCS 2368
, 2002
"... Steiner tree problem in weighted graphs seeks a minimum weight subtree containing a given subset of the vertices (terminals). We show that it is NPhard to approximate the Steiner tree problem within 96/95. Our inapproximability results are stated in parametric way and can be further improved ju ..."
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Cited by 23 (0 self)
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Steiner tree problem in weighted graphs seeks a minimum weight subtree containing a given subset of the vertices (terminals). We show that it is NPhard to approximate the Steiner tree problem within 96/95. Our inapproximability results are stated in parametric way and can be further improved just providing gadgets and/or expanders with better parameters. The reduction is from Hastad's inapproximability result for maximum satis ability of linear equations modulo 2 with three unknowns per equation. This was rst used for the Steiner tree problem by Thimm whose approach was the main starting point for our results.
Approximation Schemes for Steiner Forest on Planar Graphs and Graphs of Bounded Treewidth
, 2010
"... We give the first polynomialtime approximation scheme (PTAS) for the Steiner forest problem on planar graphs and, more generally, on graphs of bounded genus. As a first step, we show how to build a Steiner forest spanner for such graphs. The crux of the process is a clustering procedure called priz ..."
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Cited by 18 (6 self)
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We give the first polynomialtime approximation scheme (PTAS) for the Steiner forest problem on planar graphs and, more generally, on graphs of bounded genus. As a first step, we show how to build a Steiner forest spanner for such graphs. The crux of the process is a clustering procedure called prizecollecting clustering that breaks down the input instance into separate subinstances which are easier to handle; moreover, the terminals in different subinstances are far from each other. Each subinstance has a relatively inexpensive Steiner tree connecting all its terminals, and the subinstances can be solved (almost) separately. Another building block is a PTAS for Steiner forest on graphs of bounded treewidth. Surprisingly, Steiner forest is NPhard even on graphs of treewidth 3. Therefore, our PTAS for bounded treewidth graphs needs a nontrivial combination of approximation arguments and dynamic programming on the tree decomposition. We further show that Steiner forest can be solved in polynomial time for seriesparallel graphs (graphs of treewidth at most two) by a novel combination of dynamic programming and minimum cut computations, completing our thorough complexity study of Steiner forest in the range of bounded treewidth graphs, planar graphs, and bounded genus graphs.
An Approximation Algorithm for the Multicast Congestion Problem via Minimum Steiner Trees
 In 3rd International Workshop on Approximation and Randomized Algorithms in Communication Networks (ARANCE
, 2002
"... We are given a graph G = (V;E) to represent a communication network where jV j = n and jEj = m and a set of multicast requests S 1 , : : : , S k V . ..."
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Cited by 17 (3 self)
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We are given a graph G = (V;E) to represent a communication network where jV j = n and jEj = m and a set of multicast requests S 1 , : : : , S k V .
A Constant Bound on Throughput Improvement of Multicast Network Coding in Undirected Networks
, 2008
"... Recent research in network coding shows that, joint consideration of both coding and routing strategies may lead to higher information transmission rates than routing only. A fundamental question in the field of network coding is: how large can the throughput improvement due to network coding be? I ..."
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Cited by 11 (8 self)
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Recent research in network coding shows that, joint consideration of both coding and routing strategies may lead to higher information transmission rates than routing only. A fundamental question in the field of network coding is: how large can the throughput improvement due to network coding be? In this paper, we prove that in undirected networks, the ratio of achievable multicast throughput with network coding to that without network coding is bounded by a constant ratio of 2, i.e., network coding can at most double the throughput. This result holds for any undirected network topology, any link capacity configuration, any multicast group size, and any source information rate. This constant bound 2 represents the tightest bound that has been proved so far in general undirected settings, and is to be contrasted with the unbounded potential of network coding in improving multicast throughput in directed networks.
How well can PrimalDual and LocalRatio algorithms perform?
, 2007
"... We define an algorithmic paradigm, the stack model, that captures many primaldual and localratio algorithms for approximating covering and packing problems. The stack model is defined syntactically and without any complexity limitations and hence our approximation bounds are independent of the P v ..."
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Cited by 10 (4 self)
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We define an algorithmic paradigm, the stack model, that captures many primaldual and localratio algorithms for approximating covering and packing problems. The stack model is defined syntactically and without any complexity limitations and hence our approximation bounds are independent of the P vs NP question. We provide tools to bound the performance of primal dual and local ratio algorithms and supply a (log n + 1)/2 inapproximability result for set cover, a 4/3 inapproximability for min steiner tree, and a 0.913 inapproximability for interval scheduling on two machines.
Approximation Hardness for Small Occurrence Instances of NPHard Problems
, 2002
"... The paper contributes to the systematic study (started by Berman and Karpinski) of explicit approximability lower bounds for small occurrence optimization problems. We present parametrized reductions for some packing and covering problems, including 3Dimensional Matching, and prove the best know ..."
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Cited by 8 (0 self)
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The paper contributes to the systematic study (started by Berman and Karpinski) of explicit approximability lower bounds for small occurrence optimization problems. We present parametrized reductions for some packing and covering problems, including 3Dimensional Matching, and prove the best known inapproximability results even for highly restricted versions of them. For example, we show that it is NPhard to approximate Max3DM within 141 140 even on instances with exactly two occurrences of each element.
On Achieving Optimal EndtoEnd Throughput in Data Networks: Theoretical and Empirical Studies
, 2004
"... With the constraints of network topologies and link capacities, achieving the optimal endtoend throughput in data networks has been known as a fundamental but computationally hard problem. In this paper, we seek efficient solutions to the problem of achieving optimal throughput in data networks, w ..."
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Cited by 7 (2 self)
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With the constraints of network topologies and link capacities, achieving the optimal endtoend throughput in data networks has been known as a fundamental but computationally hard problem. In this paper, we seek efficient solutions to the problem of achieving optimal throughput in data networks, with single or multiple unicast, multicast and broadcast sessions. Towards this objective, we first investigate upper and lower bounds of such optimal throughput in the case of a single multicast session, and show that it is computationally hard to compute these bounds. We then show the surprising result that, facilitated by the recent advances of network coding, computing the strategies to achieve the optimal endtoend throughput can be performed in polynomial time, using the algorithm we propose. In addition, we extend our results to the cases of multiple sessions of unicast, multicast, broadcast and group communication, as well as the model of overlay networks. In all these cases, we also show that the optimal achievable throughput is independent from the selection of data sources within each session. Finally, supported by empirical studies, we present the surprising observation that in most topologies, applying network coding may not improve the achievable optimal throughput; rather, it facilitates the design of significantly more efficient algorithms to achieve such optimality. I.
A polynomialtime approximation scheme for euclidean steiner forest
 Foundations of Computer Science, Annual IEEE Symposium on
"... We give a randomized O(n polylog n)time approximation scheme for the Steiner forest problem in the Euclidean plane. For every fixed ǫ> 0 and given n terminals in the plane with connection requests between some pairs of terminals, our scheme finds a (1 + ǫ)approximation to the minimumlength forest ..."
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Cited by 6 (1 self)
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We give a randomized O(n polylog n)time approximation scheme for the Steiner forest problem in the Euclidean plane. For every fixed ǫ> 0 and given n terminals in the plane with connection requests between some pairs of terminals, our scheme finds a (1 + ǫ)approximation to the minimumlength forest that connects every requested pair of terminals. 1