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Functionalrepairbytransfer regenerating codes
 in IEEE International Symposium on Information Theory (ISIT
, 2012
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Capacity of Multiple Unicast in Wireless Networks: A Polymatroidal Approach
, 2011
"... A classical result in undirected wireline networks is the near optimality of routing (flow) for multipleunicast traffic (multiple sources communicating independent messages to multiple destinations): the min cut upper bound is within a logarithmic factor of the number of sources of the max flow. In ..."
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A classical result in undirected wireline networks is the near optimality of routing (flow) for multipleunicast traffic (multiple sources communicating independent messages to multiple destinations): the min cut upper bound is within a logarithmic factor of the number of sources of the max flow. In this paper we “extend” the wireline result to the wireless context. Our main result is the approximate optimality of a simple layering principle: local physicallayer schemes combined with global routing. We use the reciprocity of the wireless channel critically in this result. Our formal result is in the context of channel models for which “good ” local schemes, that achieve the cutset bound, exist (such as Gaussian MAC and broadcast channels, broadcast erasure networks, fast fading Gaussian networks). Layered architectures, common in the engineeringdesign of wireless networks, can have nearoptimal performance if the locality over which physicallayer schemes should operate is carefully designed. Feedback is shown to play a critical role in enabling the separation between the physical and the network layers. The key technical idea is the modeling of a wireless network by an undirected “polymatroidal” network, for which we establish a maxflow mincut approximation theorem.
The AllorNothing Flow Problem in Directed Graphs with Symmetric Demand Pairs∗
, 2014
"... We study the approximability of the AllorNothing multicommodity flow problem in directed graphs with symmetric demand pairs (SymANF). The input consists of a directed graph G = (V,E) and a collection of (unordered) pairs of nodesM = {s1t1, s2t2,..., sktk}. A subsetM ′ of the pairs is routable if t ..."
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We study the approximability of the AllorNothing multicommodity flow problem in directed graphs with symmetric demand pairs (SymANF). The input consists of a directed graph G = (V,E) and a collection of (unordered) pairs of nodesM = {s1t1, s2t2,..., sktk}. A subsetM ′ of the pairs is routable if there is a feasible multicommodity flow in G such that, for each pair siti ∈ M′, the amount of flow from si to ti is at least one and the amount of flow from ti to si is at least one. The goal is to find a maximum cardinality subset of the given pairs that can be routed. Our main result is a polylogarithmic approximation with constant congestion for SymANF. We obtain this result by extending the welllinked decomposition framework of [11] to the directed graph setting with symmetric demand pairs. We point out the importance of studying routing problems in this setting and the relevance of our result to future work. 1
Network Capacity under Traffic Symmetry: Wireline and Wireless Networks
"... The problem of designing near optimal strategies for multiple unicast traffic in wireline networks is wideopen; however, channel symmetry or traffic symmetry can be leveraged to show that routing can achieve with a polylogarithmic approximation factor of the edgecut bound. For the same problem, t ..."
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The problem of designing near optimal strategies for multiple unicast traffic in wireline networks is wideopen; however, channel symmetry or traffic symmetry can be leveraged to show that routing can achieve with a polylogarithmic approximation factor of the edgecut bound. For the same problem, the edgecut bound is known to only upper bound rates of routing flows and unlike the information theoretic cutset bound, it does not upper bound (capacityachieving) information rates with general strategies. In this paper, we demonstrate that under channel or traffic symmetry, the edgecut bound upperbounds general information rates, thus providing a capacity approximation result. The key technique is a combinatorial result relating edgecut bounds to generalized network sharing bounds. Finally, we generalize the results to wireless networks via an intermediary class of combinatorial graphs known as polymatroidal networks – our main result is that a natural architecture separating the physical and networking layers is near optimal when the traffic is symmetric among sourcedestination pairs, even when the channel is asymmetric (due to asymmetric power constraints, or prior frequency allocation like frequency division duplexing). This result is complementary to our earlier work proving a similar result under channel symmetry [1]. I.
APPROXIMATION ALGORITHMS FOR SUBMODULAR OPTIMIZATION AND GRAPH PROBLEMS
, 2013
"... In this thesis, we consider combinatorial optimization problems involving submodular functions and graphs. The problems we study are NPhard and therefore, assuming that P 6 = NP, there do not exist polynomialtime algorithms that always output an optimal solution. In order to cope with the intracta ..."
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In this thesis, we consider combinatorial optimization problems involving submodular functions and graphs. The problems we study are NPhard and therefore, assuming that P 6 = NP, there do not exist polynomialtime algorithms that always output an optimal solution. In order to cope with the intractability of these problems, we focus on algorithms that construct approximate solutions: An approximation algorithm is a polynomialtime algorithm that, for any instance of the problem, it outputs a solution whose value is within a multiplicative factor ρ of the value of the optimal solution for the instance. The quantity ρ is the approximation ratio of the algorithm and we aim to achieve the smallest ratio possible. Our focus in this thesis is on designing approximation algorithms for several combinatorial optimization problems. In the first part of this thesis, we study a class of constrained submodular minimization problems. We introduce a model that captures allocation problems with submodular costs and we give a generic approach for designing approximation algorithms for problems in this model. Our model captures several problems of interest, such as nonmetric facility location, multiway cut problems in graphs and hypergraphs, uniform metric labeling and its generalization
The AllorNothing Flow Problem in Directed Graphs with Symmetric Demand Pairs
, 2014
"... We study the approximability of the AllorNothing multicommodity flow problem in directed graphs with symmetric demand pairs (SymANF). The input consists of a directed graph G = (V,E) and a collection of (unordered) pairs of nodesM = {s1t1, s2t2,..., sktk}. A subsetM ′ of the pairs is routable if t ..."
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We study the approximability of the AllorNothing multicommodity flow problem in directed graphs with symmetric demand pairs (SymANF). The input consists of a directed graph G = (V,E) and a collection of (unordered) pairs of nodesM = {s1t1, s2t2,..., sktk}. A subsetM ′ of the pairs is routable if there is a feasible multicommodity flow in G such that, for each pair siti ∈ M′, the amount of flow from si to ti is at least one and the amount of flow from ti to si is at least one. The goal is to find a maximum cardinality subset of the given pairs that can be routed. Our main result is a polylogarithmic approximation with constant congestion for SymANF. We obtain this result by extending the welllinked decomposition framework of [11] to the directed graph setting with symmetric demand pairs. We point out the importance of studying routing problems in this setting and the relevance of our result to future work.