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58
Pebble Game Algorithms and Sparse Graphs
, 2007
"... A multigraph G on n vertices is (k,ℓ)sparse if every subset of n ′ ≤ n vertices spans at most kn ′ − ℓ edges. G is tight if, in addition, it has exactly kn − ℓ edges. For integer values k and ℓ ∈ [0,2k), we characterize the (k,ℓ)sparse graphs via a family of simple, elegant and efficient algori ..."
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Cited by 18 (6 self)
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A multigraph G on n vertices is (k,ℓ)sparse if every subset of n ′ ≤ n vertices spans at most kn ′ − ℓ edges. G is tight if, in addition, it has exactly kn − ℓ edges. For integer values k and ℓ ∈ [0,2k), we characterize the (k,ℓ)sparse graphs via a family of simple, elegant and efficient algorithms called the (k,ℓ)pebble games.
On Achieving Optimized Capacity Utilization in Application Overlay Networks with Multiple Competing Sessions
 Sessions, 16th annual ACM symposium on parallelism in algorithms and architectures (SPAA ’04
, 2004
"... In this paper, we examine the problem of largevolume data dissemination via overlay networks. A natural way to maximize the throughput of an overlay multicast session is to split the traffic and feed them into multiple trees. While in singletree solutions, bandwidth of leaf nodes may remain larg ..."
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Cited by 17 (3 self)
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In this paper, we examine the problem of largevolume data dissemination via overlay networks. A natural way to maximize the throughput of an overlay multicast session is to split the traffic and feed them into multiple trees. While in singletree solutions, bandwidth of leaf nodes may remain largely underutilized, multitree solutions increase the chances for a node to contribute its bandwidth by being a relaying node in at least one of the trees. We study the following problems: (1) What is the maximum capacity multitree solutions can exploit from overlay networks? (2) When multiple sessions compete within the same network, what is the relationship of two contradictory goals: achieving fairness and maximizing overall throughput? (3) What is the impact of IP routing in achieving at constraining the optimal performance of overlay multicast? We extend the multicommodity flow model to the case of overlay data dissemination, where each commodity is associated with an overlay session, rather than the traditional sourcedestination pair. We first prove that the problem is solvable in polynomial time, then propose an #approximation algorithm, assuming that each commodity can be split in arbitrary ways. The solution to this problem establishes the theoretical upper bound of overall throughput that any multitree solution could reach. We then study the same problem with the restriction that each commodity can only be split and fed into a limited number of trees. A randomized rounding algorithm and an online treeconstruction algorithm are presented. All these algorithms are evaluated by extensive simulations.
Lower bounds on twoterminal network reliability
, 1985
"... One measure of twoterminal network reliability, termed probabilistic connectedness, is the probability that two specified communication centers can communicate. A standard model of a network is a graph in which nodes represent communications centers and edges represent links between communication c ..."
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Cited by 14 (0 self)
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One measure of twoterminal network reliability, termed probabilistic connectedness, is the probability that two specified communication centers can communicate. A standard model of a network is a graph in which nodes represent communications centers and edges represent links between communication centers. Edges are assumed to have statistically independent probabilities of failing and nodes are assumed to be perfectly reliable. Exact calculation of twoterminal reliability for general networks has been shown to be #Pcomplete. As a result is desirable to compute upper and lower bounds that avoid the exponential computation likely required by exact algorithms. Two methods are considered for computing lower bounds on twoterminal reliability
Characterizations of arboricity of graphs
 Ars Combinatorica
"... The aim of this paper is to give several characterizations for the following two classes of graphs: (i) graphs for which adding any l edges produces a graph which is decomposible into k spanning trees and (ii) graphs for which adding some l edges produces a graph which is decomposible into k spannin ..."
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Cited by 12 (0 self)
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The aim of this paper is to give several characterizations for the following two classes of graphs: (i) graphs for which adding any l edges produces a graph which is decomposible into k spanning trees and (ii) graphs for which adding some l edges produces a graph which is decomposible into k spanning trees. Introduction and Theorems The concept of decomposing a graph into the minimum number of trees or forests dates back to NashWilliams and Tutte [6, 7, 11]. Since then, many authors have examined various tree decompositions of classes of graphs (for example [2, 8]). The aim of this paper is to give several characterizations for
NonAdaptive Fault Diagnosis for AllOptical Networks via Combinatorial Group Testing on Graphs
"... We consider the fault diagnosis problem in alloptical networks, focusing on probing schemes to detect faults. Our work concentrates on nonadaptive probing schemes, in order to meet the stringent time requirements for fault recovery. This fault diagnosis problem motivates a new technical framework ..."
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Cited by 11 (0 self)
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We consider the fault diagnosis problem in alloptical networks, focusing on probing schemes to detect faults. Our work concentrates on nonadaptive probing schemes, in order to meet the stringent time requirements for fault recovery. This fault diagnosis problem motivates a new technical framework that we introduce: group testing with graphbased constraints. Using this framework, we develop several new probing schemes to detect network faults. The efficiency of our schemes often depends on the network topology; in many cases we can show that our schemes are nearoptimal by providing tight lower bounds.
What is a matroid?
, 2007
"... Matroids were introduced by Whitney in 1935 to try to capture abstractly the essence of dependence. Whitney’s definition embraces a surprising diversity of combinatorial structures. Moreover, matroids arise naturally in combinatorial optimization since they are precisely the structures for which th ..."
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Cited by 10 (0 self)
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Matroids were introduced by Whitney in 1935 to try to capture abstractly the essence of dependence. Whitney’s definition embraces a surprising diversity of combinatorial structures. Moreover, matroids arise naturally in combinatorial optimization since they are precisely the structures for which the greedy algorithm works. This survey paper introduces matroid theory, presents some of the main theorems in the subject, and identifies some of the major problems of current research interest.
Locally finite graphs with ends: a topological approach
"... This paper is intended as an introductory survey of a newly emerging field: a topological approach to the study of locally finite graphs that crucially incorporates their ends. Topological arcs and circles, which may pass through ends, assume the role played in finite graphs by paths and cycles. Thi ..."
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Cited by 6 (6 self)
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This paper is intended as an introductory survey of a newly emerging field: a topological approach to the study of locally finite graphs that crucially incorporates their ends. Topological arcs and circles, which may pass through ends, assume the role played in finite graphs by paths and cycles. This approach has made it possible to extend to locally finite graphs many classical theorems of finite graph theory that do not extend verbatim. The shift of paradigm it proposes is thus as much an answer to old questions as a source of new ones; many concrete problems of both types are suggested in the paper. This paper attempts to provide an entry point to this field for readers that have not followed the literature that has emerged in the last 10 years or so. It takes them on a quick route through what appear to be the most important lasting results, introduces them to key proof techniques, identifies the most promising open
A necessary condition for the existence of disjoint bases of a family of infinite matroids
 CONGR. NUMERANTIUM 105 (1994)
, 1994
"... Let M = (Mr)r∈R be a system of matroids on a set S. Following the ideas of NashWilliams [7], for every transfinite sequence f of distinct elements of S, we define a number η(f). We prove that the condition that η(f) ≥ 0 for every possible choice of f is necessary for M to have a system of mutually ..."
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Cited by 6 (2 self)
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Let M = (Mr)r∈R be a system of matroids on a set S. Following the ideas of NashWilliams [7], for every transfinite sequence f of distinct elements of S, we define a number η(f). We prove that the condition that η(f) ≥ 0 for every possible choice of f is necessary for M to have a system of mutually disjoint bases. Further, we show that this condition is sufficient if R is countable and Mr is a rankfinite transversal matroid for every r ∈ R. We also present conjectures about edgedisjoint spanning trees and detachments of countable graphs.
Optimal graph orientation with storage applications, SFBReport F00351 (Optimierung und Kontrolle
, 1995
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