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Can ISPs and P2P users cooperate for improved performance
 ACM SIGCOMM Computer Communication Review
, 2007
"... This paper addresses the antagonistic relationship between overlay/p2p networks and IPS providers: they both try to manage and control traffic at different level and with different goals, but in a way that inevitably leads to overlapping, duplicated, and conflicting behavior. The creation of a p2p n ..."
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Cited by 62 (3 self)
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This paper addresses the antagonistic relationship between overlay/p2p networks and IPS providers: they both try to manage and control traffic at different level and with different goals, but in a way that inevitably leads to overlapping, duplicated, and conflicting behavior. The creation of a p2p network and the routing at the p2p layer are ultimately treading on the routing functions of ISPs. The paper proposes a solution to develop a synergistic relationship between p2p and ISPs: ISPs maintain an “oracle ” to help p2p networks in making better choices in picking neighboring nodes. The solution provides benefits to both parties. ISPs become able to influence the p2p decisions, and ultimately the amount of traffic that flows in and out of their network, while p2p networks get performance information for “free. ” The reviewers find that the problem is important and the solution is interesting and shows promise. An advantage of the method is that ISPs do not run into legal issues, since they do not engage in caching of potentially illegal content, they just provide performance information. a c m s i g c o m m Public review written by
Approximation Algorithms for the Unsplittable Flow Problem
"... We present approximation algorithms for the unsplittable flow problem (UFP) on undirected graphs. As is standard in this line of research, we assume that the maximum demand is at most the minimum capacity. We focus on the nonuniform capacity case in which the edge capacities can vary arbitrarily ..."
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Cited by 42 (7 self)
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We present approximation algorithms for the unsplittable flow problem (UFP) on undirected graphs. As is standard in this line of research, we assume that the maximum demand is at most the minimum capacity. We focus on the nonuniform capacity case in which the edge capacities can vary arbitrarily over the graph. Our results are: For undirected graphs we obtain a O(\Delta ff \Gamma 1 log2 n) approximation ratio, where n is the number of vertices, \Delta the maximum degree, and ff the expansion of the graph. Our ratio is capacity independent and improves upon the earlier O(\Delta ff \Gamma 1(c max=cmin) log n) bound [15] for large values of cmax=cmin. Furthermore, if we specialize to the case where all edges have the same capacity, our algorithm gives an O(\Delta ff \Gamma 1 log n) approximation, which matches the performance of the bestknown algorithm [15] for this special case. For certain strong constantdegree expanders considered by Frieze [10] we obtain an O(plog n) approximation for the uniform capacity case, improving upon the current O(log n) approximation. For UFP on the line and the ring, we give the first constantfactor approximation algorithms. Previous results addressed only the uniform capacity case. All of the above results improve if the maximum demand is bounded
The AllorNothing Multicommodity Flow Problem
 in Proceedings of the 36th ACM Symposium on Theory of Computing (STOC
, 2004
"... m)), the same as that for edp [10]. Our algorithm extends to the case where each pair siti has a demand di associated with it and we need to completely route di to get credit for pair i. We also consider the online admission control version where pairs arrive online and the algorithm has to decide i ..."
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Cited by 40 (10 self)
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m)), the same as that for edp [10]. Our algorithm extends to the case where each pair siti has a demand di associated with it and we need to completely route di to get credit for pair i. We also consider the online admission control version where pairs arrive online and the algorithm has to decide immediately on its arrival whether to accept it or not. We obtain a randomized algorithm with a competitive ratio that is similar to the approximation ratio for the offline algorithm. \Lambda
On the kSplittable Flow Problem
, 2002
"... In traditional multicommodity flow theory, the task is to send a certain amount of each commodity from its start to its target node, subject to capacity constraints on the edges. However, ..."
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Cited by 17 (3 self)
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In traditional multicommodity flow theory, the task is to send a certain amount of each commodity from its start to its target node, subject to capacity constraints on the edges. However,
Finding effective supporttree preconditioners
 in Proceedings of the 17th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA
, 2005
"... In 1995, Gremban, Miller, and Zagha introduced supporttree preconditioners and a parallel algorithm called supporttree conjugate gradient (STCG) for solving linear systems of the form Ax = b, where A is an n × n Laplacian matrix. A Laplacian is a symmetric matrix in which the offdiagonal entries ..."
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Cited by 11 (1 self)
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In 1995, Gremban, Miller, and Zagha introduced supporttree preconditioners and a parallel algorithm called supporttree conjugate gradient (STCG) for solving linear systems of the form Ax = b, where A is an n × n Laplacian matrix. A Laplacian is a symmetric matrix in which the offdiagonal entries are nonpositive, and the row and column sums are zero. A Laplacian A with 2m nonzeros can be interpreted as an undirected positivelyweighted graph G with n vertices and m edges, where there is an edge between two nodes i and j with weight c((i, j)) = −Ai,j = −Aj,i if Ai,j = Aj,i < 0. Gremban et al. showed experimentally that STCG performs well on several classes of graphs commonly used in scientific computations. In his thesis, Gremban also proved upper bounds on the number of iterations required for STCG to converge for certain classes of graphs. In this paper, we present an algorithm for finding a preconditioner for an arbitrary graph G = (V, E) with n nodes, m edges, and a weight function c> 0 on the edges, where w.l.o.g., mine∈E c(e) = 1. Equipped with this preconditioner, STCG requires O(log 4 n · � ∆/α) iterations, where α = min U⊂V,U≤V /2 c(U, V \U)/U  is the minimum edge expansion of the graph, and ∆ = maxv∈V c(v) is the maximum incident weight on any vertex. Each iteration requires O(m) work and can be implemented in O(log n) steps in parallel, using only O(m) space. Our results generalize to matrices that are symmetric and diagonallydominant (SDD). 1
Crossing number, paircrossing number, and expansion
 J. Combin. Theory Ser. B
, 2004
"... We also prove by similar methods that a graph G with crossing number k = cr(G) ? Cpssqd(G) m log2 n has a nonplanar subgraph on at most O\Gamma \Delta nm log2 nk \Delta vertices, where m is the number of edges, \Delta is the maximum degree in G, and C is a suitable sufficiently large constant. ..."
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Cited by 10 (0 self)
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We also prove by similar methods that a graph G with crossing number k = cr(G) ? Cpssqd(G) m log2 n has a nonplanar subgraph on at most O\Gamma \Delta nm log2 nk \Delta vertices, where m is the number of edges, \Delta is the maximum degree in G, and C is a suitable sufficiently large constant.
Algorithms for FaultTolerant Routing in Circuit Switched Networks (Extended Abstract)
 In Proceedings of 14th Annual ACM Symposium on Parallel Algorithms and Architectures
, 2002
"... Amitabha Bagchi, Amitabh Chaudhary, and Christian Scheideler Dept. of Computer Science Johns Hopkins University 3400 N. Charles Street Baltimore, MD 21218, USA {bagchi,amic,scheideler}@cs.jhu.edu Petr Kolman Inst. for Theoretical Computer Science Charles University Malostransk e n am. 25 1 ..."
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Cited by 10 (4 self)
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Amitabha Bagchi, Amitabh Chaudhary, and Christian Scheideler Dept. of Computer Science Johns Hopkins University 3400 N. Charles Street Baltimore, MD 21218, USA {bagchi,amic,scheideler}@cs.jhu.edu Petr Kolman Inst. for Theoretical Computer Science Charles University Malostransk e n am. 25 118 00 Prague, Czech Republic kolman@kam.mff.cuni.cz ABSTRACT In this paper we consider the k edgedisjoint paths problem (kEDP), a generalization of the wellknown edgedisjoint paths problem. Given a graph G = (V, E) and a set of terminal pairs (or requests) T , the problem is to find a maximum subset of the pairs in T for which it is possible to select paths such that each pair is connected by k edgedisjoint paths and the paths for di#erent pairs are mutually disjoint. To the best of our knowledge, no nontrivial result is known for this problem for k > 1. To measure the performance of our algorithms we will use the recently introduced flow number F of a graph. This parameter is known to fulfill F = O(## 1 log n), where # is the maximum degree and # is the edge expansion of G. We show that a simple, greedy online algorithm achieves a competitive ratio of F ), which naturally extends the best known bound of O(F ) for k = 1 to higher k. To achieve this competitive ratio, we introduce a new method of converting a system of k disjoint paths into a system of k lengthbounded disjoint paths. We also show that any deterministic online algorithm has a competitive ratio of ## k F ).
Short Length Menger's Theorem and Reliable Optical Routing
 Theoretical Computer Science
, 2003
"... In the minimum path coloring problem, we are given a graph and a set of pairs of vertices of the graph and we are asked to connect the pairs by colored paths in such a way that paths of the same color are edge disjoint. In this paper we deal with a generalization of this problem where we are aske ..."
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Cited by 10 (3 self)
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In the minimum path coloring problem, we are given a graph and a set of pairs of vertices of the graph and we are asked to connect the pairs by colored paths in such a way that paths of the same color are edge disjoint. In this paper we deal with a generalization of this problem where we are asked to connect each pair by a k edge disjoint paths of the same color. The objective is to minimize the number of colors. The reason for multiple paths between the same pair of vertices is to ensure fault tolerance of the connections. We propose an O(k ## 1 log n) approximation algorithm for this problem where F is the flow number of the graph, # is the maximum degree and # is the expansion. This is an improvement even for the special case k = 1 where, to our knowledge, the best bound known previously is weaker by a factor of log n.
Flows on Few Paths: Algorithms and Lower Bounds
, 2004
"... Classical network flow theory allows decomposition of flow into several chunks of arbitrary sizes traveling through the network on different paths. In the first part of this paper we consider the unsplittable flow problem where all flow traveling from a source to a destination must be sent on only ..."
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Cited by 9 (1 self)
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Classical network flow theory allows decomposition of flow into several chunks of arbitrary sizes traveling through the network on different paths. In the first part of this paper we consider the unsplittable flow problem where all flow traveling from a source to a destination must be sent on only one path. We prove a lower bound of Ω(log m / log log m) on the performance of a general class of algorithms for minimizing congestion where m is the number of edges in a graph. These algorithms start with a solution for the classical multicommodity flow problem, compute a path decomposition, and select one of its paths for each commodity in order to obtain an unsplittable flow. Our result matches the best known upper bound for randomized rounding – an algorithm of this type introduced by Raghavan and Thompson. The ksplittable flow problem is a generalization of the unsplittable flow problem where the number of paths is bounded for each commodity. We study a new variant of this problem with additional constraints on the amount of flow being sent along each path. We present approximation results for two versions of this problem with the objective to minimize the congestion of the network. The key idea is to reduce the problem under consideration to an unsplittable flow problem while only losing a constant factor in the performance ratio.