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On the Capacity of Information Networks
"... An outer bound on the rate region of noisefree information networks is given. This outer bound combines properties of entropy with a strong information inequality derived from the structure of the network. This blend of information theoretic and graph theoretic arguments generates many interestin ..."
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Cited by 94 (8 self)
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An outer bound on the rate region of noisefree information networks is given. This outer bound combines properties of entropy with a strong information inequality derived from the structure of the network. This blend of information theoretic and graph theoretic arguments generates many interesting results. For example, the capacity of directed cycles is characterized. Also, a gap between the sparsity of an undirected graph and its capacity is shown. Extending this result, it is shown that multicommodity flow solutions achieve the capacity in an infinite class of undirected graphs, thereby making progress on a conjecture of Li and Li. This result is in sharp contrast to the situation with directed graphs, where a family of graphs are presented in which the gap between the capacity and the rate achievable using multicommodity flows is linear in the size of the graph.
NonCooperative Multicast and Facility Location Games
"... We consider a multicast game with selfish noncooperative players. There is a special source node and each player is interested in connecting to the source by making a routing decision that minimizes its payment. The mutual influence of the players is determined by a cost sharing mechanism, which in ..."
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Cited by 41 (2 self)
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We consider a multicast game with selfish noncooperative players. There is a special source node and each player is interested in connecting to the source by making a routing decision that minimizes its payment. The mutual influence of the players is determined by a cost sharing mechanism, which in our case evenly splits the cost of an edge among the players using it. We consider two different models: an integral model, where each player connects to the source by choosing a single path, and a fractional model, where a player is allowed to split the flow it receives from the source between several paths. In both models we explore the overhead incurred in network cost due to the selfish behavior of the users, as well as the computational complexity of finding a Nash equilibrium. The existence of a Nash equilibrium for the integral model was previously established by the means of a potential function. We prove that finding a Nash equilibrium that minimizes the potential function is NPhard. We focus on the price of anarchy of a Nash equilibrium resulting from the bestresponse dynamics of a game course, where the players join the game sequentially. For a game with n players, we establish an upper bound of O ( √ n log 2 n) on the price of anarchy, and a lower bound of Ω(log n/log log n). For the fractional model, we prove the existence of a Nash equilibrium via a potential function and give a polynomial time algorithm for computing an equilibrium that minimizes the potential function. Finally, we consider a weighted extension of the multicast game, and prove that in the fractional model, the game always has a Nash equilibrium.
On Achieving Maximum Multicast Throughput in Undirected Networks
 IEEE/ACM TRANS. NETWORKING
, 2006
"... The transmission of information within a data network is constrained by the network topology and link capacities. In this paper, we study the fundamental upper bound of information dissemination rates with these constraints in undirected networks, given the unique replicable and encodable propertie ..."
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Cited by 36 (5 self)
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The transmission of information within a data network is constrained by the network topology and link capacities. In this paper, we study the fundamental upper bound of information dissemination rates with these constraints in undirected networks, given the unique replicable and encodable properties of information flows. Based on recent advances in network coding and classical modeling techniques in flow networks, we provide a natural linear programming formulation of the maximum multicast rate problem. By applying Lagrangian relaxation on the primal and the dual linear programs (LPs), respectively, we derive a) a necessary and sufficient condition characterizing multicast rate feasibility, and b) an efficient and distributed subgradient algorithm for computing the maximum multicast rate. We also extend our discussions to multiple communication sessions, as well as to overlay and ad hoc network models. Both our theoretical and simulation results conclude that, network coding may not be instrumental to achieve better maximum multicast rates in most cases; rather, it facilitates the design of significantly more efficient algorithms to achieve such optimality.
Network Coding for Joint Storage and Transmission with Minimum Cost
 In ISIT
, 2006
"... Abstract — Network coding provides elegant solutions to many data transmission problems. The usage of coding for distributed data storage has also been explored. In this work, we study a joint storage and transmission problem, where a source transmits a file to storage nodes whenever the file is upd ..."
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Cited by 33 (0 self)
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Abstract — Network coding provides elegant solutions to many data transmission problems. The usage of coding for distributed data storage has also been explored. In this work, we study a joint storage and transmission problem, where a source transmits a file to storage nodes whenever the file is updated, and clients read the file by retrieving data from the storage nodes. The cost includes the transmission cost for file update and file read, as well as the storage cost. We show that such a problem can be transformed into a pure flow problem and is solvable in polynomial time using linear programming. Coding is often necessary for obtaining the optimal solution with the minimum cost. However, we prove that for networks of generalized tree structures, where adjacent nodes can have asymmetric links between them, file splitting — instead of coding — is sufficient for achieving optimality. In particular, if there is no constraint on the numbers of bits that can be stored in storage nodes, there exists an optimal solution that always transmits and stores the file as a whole. The proof is accompanied by an algorithm that optimally assigns file segments to storage nodes. I.
On the capacity of multiple unicast sessions in undirected graphs
 IEEE Transactions on Information Theory
, 2005
"... Abstract — Li and Li conjectured that in an undirected network with multiple unicast sessions, network coding does not lead to any coding gain. Surprisingly enough, this conjecture could not so far be verified even for the simple network consisting of K3,2 with four sourcesink pairs. Using entropy ..."
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Cited by 24 (1 self)
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Abstract — Li and Li conjectured that in an undirected network with multiple unicast sessions, network coding does not lead to any coding gain. Surprisingly enough, this conjecture could not so far be verified even for the simple network consisting of K3,2 with four sourcesink pairs. Using entropy calculus, we provide the first verification of the Li–Li conjecture for this network. We extend our bound to the case of an arbitrary directed bipartite network. I.
On Average Throughput and Alphabet Size in Network Coding
 IEEE TRANSACTION ON INFORMATION THEORY (TO APPEAR)
, 2005
"... We examine the throughput benefits that network coding offers with respect to the average throughput achievable by routing, where the average throughput refers to the average of the rates that the individual receivers experience. We relate these benefits to the integrality gap of a standard LP for ..."
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Cited by 22 (2 self)
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We examine the throughput benefits that network coding offers with respect to the average throughput achievable by routing, where the average throughput refers to the average of the rates that the individual receivers experience. We relate these benefits to the integrality gap of a standard LP formulation for the directed Steiner tree problem. We describe families of configurations over which network coding at most doubles the average throughput, and analyze a class of directed graph configurations with N receivers where network coding offers benefits proportional to √ N. We also discuss other throughput measures in networks, and show how in certain classes of networks, average throughput bounds can be translated into minimum throughput bounds, by employing vector routing and channel coding. Finally, we show configurations where use of randomized coding may require an alphabet size exponentially larger than the minimum alphabet size required.
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
On the Multiple Unicast Network Coding Conjecture
"... Abstract—In this paper, we study the multiple unicast network communication problem on undirected graphs. It has been conjectured by Li and Li [CISS 2004] that, for the problem at hand, the use of network coding does not allow any advantage over standard routing. Loosely speaking, we show that under ..."
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Cited by 17 (3 self)
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Abstract—In this paper, we study the multiple unicast network communication problem on undirected graphs. It has been conjectured by Li and Li [CISS 2004] that, for the problem at hand, the use of network coding does not allow any advantage over standard routing. Loosely speaking, we show that under certain (strong) connectivity requirements the advantage of network coding is indeed bounded by 3. I.
Bounding The Coding Advantage of Combination Network Coding in Undirected Networks
 IEEE TRANSACTIONS ON INFORMATION THEORY
"... We refer to network coding schemes in which information flows propagate along a combination network topology as combination network coding (CNC). CNC and its variations are the first network coding schemes studied in the literature, and so far still represent arguably the most important class of kno ..."
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Cited by 13 (8 self)
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We refer to network coding schemes in which information flows propagate along a combination network topology as combination network coding (CNC). CNC and its variations are the first network coding schemes studied in the literature, and so far still represent arguably the most important class of known structures where network coding is nontrivial. Our main goal in this paper is to seek a thorough understanding on the advantage of CNC in undirected networks, by proving a tight bound on its potential both in improving multicast throughput (the coding advantage) and in reducing multicast cost under a linear link flow cost model (the cost advantage). We prepare three results towards this goal. First, we show that the cost advantage of CNC is upperbounded by 9 8 under the uniform link cost setting. Second, we show that achieving a larger cost advantage is impossible by considering an arbitrary instead of uniform link cost configuration. Third, we show that in a given network topology, for any form of network coding, the coding advantage under arbitrary link capacity configurations is always upperbounded by the cost advantage under arbitrary link cost configurations. Combining the three results together, we conclude that the potential for CNC to improve throughput and to reduce routing cost are both upperbounded by a factor of 9 8. The bound is tight since it is achieved in specific networks. This result can be viewed as a natural step towards improving the bound of 2 proved for the coding advantage of general multicast network coding.