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35
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 493 (7 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.
Cooperative security for network coding file distribution," in
 Proc. of IEEE INFOCOM'06,
, 2006
"... AbstractPeertopeer content distribution networks can suffer from malicious participants that intentionally corrupt content. Traditional systems verify blocks with traditional cryptographic signatures and hashes. However, these techniques do not apply well to more elegant schemes that use network ..."
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Cited by 109 (2 self)
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AbstractPeertopeer content distribution networks can suffer from malicious participants that intentionally corrupt content. Traditional systems verify blocks with traditional cryptographic signatures and hashes. However, these techniques do not apply well to more elegant schemes that use network coding techniques for efficient content distribution. Architectures that use network coding are prone to jamming attacks where the introduction of a few corrupted blocks can quickly result in a large number of bad blocks propagating through the system. Identifying such bogus blocks is difficult and requires the use of homomorphic hashing functions, which are computationally expensive. This paper presents a practical security scheme for network coding that reduces the cost of verifying blocks onthefly while efficiently preventing the propagation of malicious blocks. In our scheme, users not only cooperate to distribute the content, but (wellbehaved) users also cooperate to protect themselves against malicious users by informing affected nodes when a malicious block is found. We analyze and study such cooperative security scheme and introduce elegant techniques to prevent DoS attacks. We show that the loss in the efficiency caused by the attackers is limited to the effort the attackers put to corrupt the communication, which is a natural lower bound in the damage of the system. We also show experimentally that checking as low as 15% of the received blocks is enough to guarantee low corruption rates.
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 79 (18 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.
On The Approximability Of The Traveling Salesman Problem
 Proceedings of the 32nd Annual ACM Symposium on Theory of Computing
, 2000
"... We show that the traveling salesman problem with triangle inequality cannot be approximated with a ratio better than 116 when the edge lengths are allowed to be asymmetric and 219 when the edge lengths are symmetric. The best previous lower bounds were 2804 and 3812 respectively. The reduction is fr ..."
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Cited by 41 (0 self)
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We show that the traveling salesman problem with triangle inequality cannot be approximated with a ratio better than 116 when the edge lengths are allowed to be asymmetric and 219 when the edge lengths are symmetric. The best previous lower bounds were 2804 and 3812 respectively. The reduction is from Håstad's maximum satisfiability of linear equations modulo 2, and is nonconstructive.
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 34 (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 27 (7 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 21 (5 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 21 (11 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.
Crossmonotonic multicast
"... In the routing and cost sharing of multicast towards a group of potential receivers, crossmonotonicity is a property that states a user’s payment can only be smaller when serviced in a larger set. Being crossmonotonic has been shown to be the key in achieving groupstrategyproofness. We study mul ..."
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Cited by 18 (2 self)
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In the routing and cost sharing of multicast towards a group of potential receivers, crossmonotonicity is a property that states a user’s payment can only be smaller when serviced in a larger set. Being crossmonotonic has been shown to be the key in achieving groupstrategyproofness. We study multicast schemes that target optimal flow routing, crossmonotonic cost sharing, and budget balance. We show that no multicast scheme can satisfy these three properties simultaneously, and resort to approximate budget balance instead. We derive both positive and negative results that complement each other for directed and undirected networks. We show that in directed networks, no crossmonotonic scheme can recover a constant fraction of optimal multicast cost. We provide a simple scheme that does achieve 1budgetbalance, where k is the number of receivers. Using a
Approximation Hardness for Small Occurrence Instances of NPHard Problems,
, 2002
"... Abstract. 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 b ..."
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Cited by 12 (0 self)
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Abstract. 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 139 138 even on instances with exactly two occurrences of each element. Previous known hardness results for bounded occurence case of the problem required that the bound is at least three, and even then no explicit lower bound was known. New structural results which improve the known bounds for 3regular amplifiers and hence the inapproximability results for numerous small occurrence problems studied earlier by Berman and Karpinski are also presented.