Results 1  10
of
27
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 ..."
Abstract

Cited by 55 (9 self)
 Add to MetaCart
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
Efficient lookup on unstructured topologies
, 2005
"... We present LMS, a protocol for efficient lookup on unstructured networks. Our protocol uses a virtual namespace without imposing specific topologies. It is more efficient than existing lookup protocols for unstructured networks, and thus is an attractive alternative for applications in which the top ..."
Abstract

Cited by 36 (8 self)
 Add to MetaCart
We present LMS, a protocol for efficient lookup on unstructured networks. Our protocol uses a virtual namespace without imposing specific topologies. It is more efficient than existing lookup protocols for unstructured networks, and thus is an attractive alternative for applications in which the topology cannot be structured as a Distributed Hash Table (DHT). We present analytic bounds for the worstcase performance of our protocol. Through detailed simulations (with up to 100,000 nodes), we show that the actual performance on realistic topologies is significantly better. We also show in both simulations and a complete implementation (which includes over five hundred nodes) that our protocol is inherently robust against multiple node failures and can adapt its replication strategy to optimize searches according to a specific heuristic. Moreover, the simulation demonstrates the resilience of LMS to high node turnover rates, and that it can easily adapt to orders of magnitude changes in network size. The overhead incurred by LMS is small, and its performance approaches that of DHTs on networks of similar size.
New Algorithmic Aspects Of The Local Lemma With Applications To Routing And Partitioning
"... . The Lov'asz Local Lemma (LLL) is a powerful tool that is increasingly playing a valuable role in computer science. The original lemma was nonconstructive; a breakthrough of Beck and its generalizations (due to Alon and Molloy & Reed) have led to constructive versions. However, these metho ..."
Abstract

Cited by 31 (6 self)
 Add to MetaCart
. The Lov'asz Local Lemma (LLL) is a powerful tool that is increasingly playing a valuable role in computer science. The original lemma was nonconstructive; a breakthrough of Beck and its generalizations (due to Alon and Molloy & Reed) have led to constructive versions. However, these methods do not capture some classes of applications of the LLL. We make progress on this, by providing algorithmic approaches to two families of applications of the LLL. The first provides constructive versions of certain applications of an extension of the LLL (modeling, e.g., hypergraphpartitioning and lowcongestion routing problems); the second provides new algorithmic results on constructing disjoint paths in graphs. Our results can also be seen as constructive upper bounds on the integrality gap of certain packing problems. One common theme of our work is a "gradual rounding" approach.
Subpath Protection for Scalability and Fast Recovery in Optical . . .
, 2004
"... This paper investigates survivable lightpath provisioning and fast protection switching for generic meshbased optical networks employing wavelengthdivision multiplexing (WDM). We propose subpath protection, which is a generalization of sharedpath protection. The main ideas of subpath protection ..."
Abstract

Cited by 27 (7 self)
 Add to MetaCart
This paper investigates survivable lightpath provisioning and fast protection switching for generic meshbased optical networks employing wavelengthdivision multiplexing (WDM). We propose subpath protection, which is a generalization of sharedpath protection. The main ideas of subpath protection are: 1) to partition a large optical network into smaller domains and 2) to apply sharedpath protection to the optical network such that an intradomain lightpath does not use resources of other domains and the primary/backup paths of an interdomain lightpath exit a domain (and enter another domain) through a common domainborder node. We mathematically formulate the routing and wavelengthassignment (RWA) problem under subpath protection for a given set of lightpath requests, prove that the problem is NPcomplete, and develop a heuristic to find efficient solutions. Comparisons between subpath protection and sharedpath protection on a nationwide network with dozens of wavelengths per fiber show that, for a modest sacrifice in resource utilization, subpath protection achieves improved survivability, much higher scalability, and significantly reduced faultrecovery time.
A polylogarithimic approximation algorithm for edgedisjoint paths with congestion 2
 IN PROC. OF IEEE FOCS
, 2012
"... In the EdgeDisjoint Paths with Congestion problem (EDPwC), we are given an undirected nvertex graph G, a collection M = {(s1, t1),..., (sk, tk)} of demand pairs and an integer c. The goal is to connect the maximum possible number of the demand pairs by paths, so that the maximum edge congestion ..."
Abstract

Cited by 10 (3 self)
 Add to MetaCart
In the EdgeDisjoint Paths with Congestion problem (EDPwC), we are given an undirected nvertex graph G, a collection M = {(s1, t1),..., (sk, tk)} of demand pairs and an integer c. The goal is to connect the maximum possible number of the demand pairs by paths, so that the maximum edge congestion the number of paths sharing any edge is bounded by c. When the maximum allowed congestion is c = 1, this is the classical EdgeDisjoint Paths problem (EDP). The best current approximation algorithm for EDP achieves an O ( √ n)approximation, by rounding the standard multicommodity flow relaxation of the problem. This matches the Ω ( √ n) lower bound on the integrality gap of this relaxation. We show an O(poly log k)approximation algorithm for EDPwC with congestion c = 2, by rounding the same multicommodity flow relaxation. This gives the best possible congestion for a subpolynomial approximation of EDPwC via this relaxation. Our results are also close to optimal in terms of the number of pairs routed, since EDPwC is known to be hard to approximate to within a factor of ˜ ( Ω (log n) 1/(c+1) for any constant congestion c. Prior to our work, the best approximation factor for EDPwC with congestion 2 was Õ(n 3/7), and the best algorithm achieving a polylogarithmic approximation required congestion 14.
Routing in undirected graphs with constant congestion
 CoRR
"... Given an undirected graph G = (V, E), a collection (s1, t1),..., (sk, tk) of k demand pairs, and an integer c, the goal in the Edge Disjoint Paths with Congestion problem is to connect maximum possible number of the demand pairs by paths, so that the maximum load on any edge (called edge congestion) ..."
Abstract

Cited by 10 (5 self)
 Add to MetaCart
Given an undirected graph G = (V, E), a collection (s1, t1),..., (sk, tk) of k demand pairs, and an integer c, the goal in the Edge Disjoint Paths with Congestion problem is to connect maximum possible number of the demand pairs by paths, so that the maximum load on any edge (called edge congestion) does not exceed c. We show an efficient randomized algorithm to route Ω(OPT / poly log k) demand pairs with congestion at most 14, where OPT is the maximum number of pairs that can be simultaneously routed on edgedisjoint paths. The best previous algorithm that routed Ω(OPT / poly log n) pairs required congestion poly(log log n), and for the setting where the maximum allowed congestion is bounded by a constant c, the best previous algorithms could only guarantee the routing of OPT/n O(1/c) pairs. We also introduce a new type of vertex sparsifiers that we call integral flow sparsifiers, that approximately preserve both fractional and integral routings, and show an algorithm to construct such sparsifiers.
Communication lower bounds via critical block sensitivity
 In Proc. 46th Annual ACM Symposium on Theory of Computing (STOC ’14
, 2014
"... Abstract. We use critical block sensitivity, a new complexity measure introduced by Huynh and Nordström (STOC 2012), to study the communication complexity of search problems. To begin, we give a simple new proof of the following central result of Huynh and Nordström: if S is a search problem with ..."
Abstract

Cited by 7 (0 self)
 Add to MetaCart
Abstract. We use critical block sensitivity, a new complexity measure introduced by Huynh and Nordström (STOC 2012), to study the communication complexity of search problems. To begin, we give a simple new proof of the following central result of Huynh and Nordström: if S is a search problem with critical block sensitivity b, then every randomised twoparty protocol solving a certain twoparty lift of S requires Ω(b) bits of communication. Besides simplicity, our proof has the advantage of generalising to the multiparty setting. We combine these results with new critical block sensitivity lower bounds for Tseitin and Pebbling search problems to obtain the following applications. • Monotone circuit depth: We exhibit a monotone function on n variables whose monotone circuits require depth Ω(n / log n); previously, a bound of Ω( n) was known (Raz and Wigderson, JACM 1992). Moreover, we prove a tight Θ( n) monotone depth bound for a function in monotone P. This implies an averagecase hierarchy theorem within monotone P similar to a result of Filmus et al. (FOCS 2013). • Proof complexity: We prove new rank lower bounds as well as obtain the first length–space lower bounds for semialgebraic proof systems, including Lovász– Schrijver and Lasserre (SOS) systems. In particular, these results extend and simplify the works of Beame et al. (SICOMP 2007) and Huynh and Nordström.ar
An algorithmic Friedman–Pippenger theorem on tree embeddings and applications to routing
 In SODA ’06: Proceedings of the seventeenth annual ACMSIAM symposium on Discrete algorithm
, 2006
"... Abstract. An (n, d)expander is a graph G = (V, E) such that for every X ⊆ V with X  ≤ 2n − 2 we have ΓG(X)  ≥ (d+1)X. A tree T is small if it has at most n vertices and has maximum degree at most d. Friedman and Pippenger (1987) proved that any (n, d)expander contains every small tree. How ..."
Abstract

Cited by 6 (2 self)
 Add to MetaCart
Abstract. An (n, d)expander is a graph G = (V, E) such that for every X ⊆ V with X  ≤ 2n − 2 we have ΓG(X)  ≥ (d+1)X. A tree T is small if it has at most n vertices and has maximum degree at most d. Friedman and Pippenger (1987) proved that any (n, d)expander contains every small tree. However, their elegant proof does not seem to yield an efficient algorithm for obtaining the tree. In this paper, we give an alternative result that does admit a polynomial time algorithm for finding the immersion of any small tree in subgraphs G of (N, D, λ)graphs Λ, as long as G contains a positive fraction of the edges of Λ and λ/D is small enough. In several applications of the Friedman–Pippenger theorem, including the ones in the original paper of those authors, the (n, d)expander G is a subgraph of an (N, D, λ)graph as above. Therefore, our result suffices to provide efficient algorithms for such previously nonconstructive applications. As an example, we discuss a recent result of Alon, Krivelevich, and Sudakov concerning embedding nearly spanning bounded degree trees, the proof of which makes use of the Friedman–Pippenger theorem. We shall also show a construction inspired on Wigderson–Zuckerman expander graphs for which any sufficiently dense subgraph contains all trees of sizes and maximum degrees achieving essentially optimal parameters. Our algorithmic approach is based on a reduction of the tree embedding problem to a certain online matching problem for bipartite graphs, solved by Aggarwal et al. (1996). 1.
Locating a Target with an Agent Guided by Unreliable Local Advice
 In Proceedings of the 29th Annual ACM SIGACTSIGOPS Symposium on Principles of Distributed Computing PODC 2010
, 2010
"... We study the problem of finding a destination node t by a mobile agent in an unreliable network having the structure of an unweighted graph, in a model first proposed by Hanusse et al. [21, 20]. Each node is able to give advice concerning the next node to visit so as to go closer to the target t. Un ..."
Abstract

Cited by 4 (1 self)
 Add to MetaCart
(Show Context)
We study the problem of finding a destination node t by a mobile agent in an unreliable network having the structure of an unweighted graph, in a model first proposed by Hanusse et al. [21, 20]. Each node is able to give advice concerning the next node to visit so as to go closer to the target t. Unfortunately, exactly k of the nodes, called liars, give advice which is incorrect. It is known that for an nnode graph G of maximum degree ∆ ≥ 3, reaching a target at a distance of d from the initial location may require an expected time of 2 Ω(min{d,k}) , for any d, k = O(log n), even when G is a tree. This paper focuses on strategies which efficiently solve the search problem in scenarios in which, at each node, the agent may only choose between following the local advice, or randomly selecting an incident edge. The strategy which we put forward, called R/A, makes use of a timer (step counter) to alternate between phases of ignoring advice (R) and following advice (A) for a certain number of steps. No knowledge of parameters n, d, or k is required, and the agent need not know by which edge it entered the node of its current location. The performance of this strategy is studied for two classes of regular graphs with extremal values of expansion, namely, for rings and for random ∆regular graphs (an important class of expanders). For the ring, R/A is shown to achieve an expected searching time of 2d+k Θ(1) for a worstcase distribution of liars, which is polynomial in both d and k. For random ∆regular graphs, the expected searching time of the R/A strategy is O(k 3 log 3 n) a.a.s. The polylogA full version of this paper is available online [19]