Results 1  10
of
41
Improved Bounds for the Unsplittable Flow Problem
 In Proceedings of the 13th ACMSIAM Symposium on Discrete Algorithms
, 2002
"... In this paper we consider the unsplittable ow problem (UFP): given a directed or undirected network G = (V, E) with edge capacities and a set of terminal pairs (or requests) with associated demands, find a subset of the pairs of maximum total demand for which a single flow path can be chosen for eac ..."
Abstract

Cited by 56 (6 self)
 Add to MetaCart
(Show Context)
In this paper we consider the unsplittable ow problem (UFP): given a directed or undirected network G = (V, E) with edge capacities and a set of terminal pairs (or requests) with associated demands, find a subset of the pairs of maximum total demand for which a single flow path can be chosen for each pair so that for every edge, the sum of the demands of the paths crossing the edge does not exceed its capacity.
Better approximation guarantees for jobshop scheduling
 SIAM Journal on Discrete Mathematics
, 1997
"... Abstract. Jobshop scheduling is a classical NPhard problem. Shmoys, Stein, and Wein presented the first polynomialtime approximation algorithm for this problem that has a good (polylogarithmic) approximation guarantee. We improve the approximation guarantee of their work and present further impro ..."
Abstract

Cited by 31 (2 self)
 Add to MetaCart
(Show Context)
Abstract. Jobshop scheduling is a classical NPhard problem. Shmoys, Stein, and Wein presented the first polynomialtime approximation algorithm for this problem that has a good (polylogarithmic) approximation guarantee. We improve the approximation guarantee of their work and present further improvements for some important NPhard special cases of this problem (e.g., in the preemptive case where machines can suspend work on operations and later resume). We also present NC algorithms with improved approximation guarantees for some NPhard special cases.
Pagoda: A dynamic overlay network for routing, data management, and multicasting
 Proceedings of the 16th Annual ACM Symposium on Parallel Algorithms and Architectures
, 2004
"... The tremendous growth of public interest in peertopeer systems in recent years has initiated a lot of research work on how to design efficient and robust overlay networks for these systems. While a large collection of scalable peertopeer overlay networks has been proposed in recent years, many f ..."
Abstract

Cited by 18 (12 self)
 Add to MetaCart
(Show Context)
The tremendous growth of public interest in peertopeer systems in recent years has initiated a lot of research work on how to design efficient and robust overlay networks for these systems. While a large collection of scalable peertopeer overlay networks has been proposed in recent years, many fundamental questions have remained open. Some of these are: • Is it possible to design deterministic peertopeer overlay networks with properties comparable to randomized peertopeer systems? • How can peers of nonuniform bandwidth be organized in an overlay network? We propose a dynamic overlay network called Pagoda that provides solutions to both of these problems. The Pagoda network has a constant degree, a logarithmic diameter, and a 1/logarithmic expansion, and therefore matches the properties of the best randomized overlay networks known so far. However, in contrast to these networks, the Pagoda is deterministic and therefore guarantees these properties. The Pagoda can be used to organize both nodes with uniform bandwidth and nodes with nonuniform bandwidth. For nodes with uniform bandwidth, any node insertion or deletion can be executed with logarithmic work, and for nodes with nonuniform bandwidth, any node insertion and deletion can be executed with polylogarithmic work. Moreover, the Pagoda overlay network can route arbitrary multicast problems with a congestion that is within a logarithmic factor of what a best possible overlay network of logarithmic degree for that particular multicast problem can achieve, even though the Pagoda is a constant degree network. This holds even for nodes of arbitrary nonuniform bandwidths. We also show that the Pagoda network can be used for efficient data management.
Fast Algorithms for Finding O(Congestion+Dilation) Packet Routing Schedules
 Combinatorica
, 1995
"... In 1988, Leighton, Maggs, and Rao showed that for any network and any set of packets whose paths through the network are fixed and edgesimple, there exists a schedule for routing the packets to their destinations in O(c + d) steps using constantsize queues, where c is the congestion of the paths ..."
Abstract

Cited by 17 (1 self)
 Add to MetaCart
In 1988, Leighton, Maggs, and Rao showed that for any network and any set of packets whose paths through the network are fixed and edgesimple, there exists a schedule for routing the packets to their destinations in O(c + d) steps using constantsize queues, where c is the congestion of the paths in the network, and d is the length of the longest path. The proof, however, used the Lovdsz Local Lemma and was not constructive. In this paper, we show how to find such a schedule in O(NE + E 1og’E) time, for any fixed 6> 0, where N is the total number of packets, and E is the number of edges in the network. We also show how to parallelize the algorithm so that it runs in NC. The method that we use to construct eficient packet routing schedules is based on the algorithmic form of the Lovdsz Local Lemma discovered by Beck. 1
Simple Online Algorithms for the Maximum Disjoint Paths Problem
 Algorithmica
, 2001
"... In this paper we study the classical problem of finding disjoint paths in graphs. This problem has been studied by a number of authors both for specific graphs and general classes of graphs. Whereas for specific graphs many (almost) matching upper and lower bounds are known for the competitivenes ..."
Abstract

Cited by 14 (2 self)
 Add to MetaCart
In this paper we study the classical problem of finding disjoint paths in graphs. This problem has been studied by a number of authors both for specific graphs and general classes of graphs. Whereas for specific graphs many (almost) matching upper and lower bounds are known for the competitiveness of online algorithms, not much is known about how well online algorithms can perform in the general setting. In several papers the expansion has been used to measure the performance of offline and online algorithms in this field. We study a class of simple deterministic online algorithms, called bounded greedy algorithms, and show that they achieve a competitive ratio that is asymptotically equal to the best possible competitive ratio that can be achieved by any deterministic online algorithm. For this we use a parameter called routing number that allows more precise results than the expansion. Interestingly, our upper bound on the competitive ratio is even better than the best approximation ratio known for offline algorithms. Furthermore, we introduce a refined variant of the routing number and show that this variant allows to construct online algorithms with a competitive ratio that can be significantly below the best possible upper bound for deterministic online algorithms if only the routing number or expansion of a network is known. We also show that our online algorithms can be transformed into efficient algorithms for the related unsplittable flow problem.
Shortest paths routing in arbitrary networks
 JOURNAL OF ALGORITHMS
, 1999
"... We introduce an online protocol which routes any set of N packets along shortest paths with congestion C and dilation D through an arbitrary network in OC � Ž D � log N. steps, with high probability. This time bound is optimal up to the additive log N, and it has previously only been reached for bo ..."
Abstract

Cited by 12 (2 self)
 Add to MetaCart
We introduce an online protocol which routes any set of N packets along shortest paths with congestion C and dilation D through an arbitrary network in OC � Ž D � log N. steps, with high probability. This time bound is optimal up to the additive log N, and it has previously only been reached for boundeddegree leveled networks. Further, we show that the preceding bound holds also for random routing problems with C denoting the maximum expected congestion over all links. Based on this result, we give applications for random routing in Cayley networks, general node symmetric networks, edge symmetric networks, and de Bruijn networks. Finally, we examine the problems arising when our approach is applied to routing along nonshortest paths, deterministic routing, or routing with bounded buffers.
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 ..."
Abstract

Cited by 10 (3 self)
 Add to MetaCart
(Show Context)
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 ).
On the Benefit of Supporting Virtual Channels in Wormhole Routers
 In Proceedings of the 8th Annual ACM Symposium on Parallel Algorithms and Architectures
, 1996
"... This paper analyzes the impact of virtual channels on the performance of wormhole routing algorithms. We show that in any network in which each physical channel, i.e., communication link, can support up to B virtual channels, it is possible to route any set of messages with L flits each, whose paths ..."
Abstract

Cited by 10 (4 self)
 Add to MetaCart
This paper analyzes the impact of virtual channels on the performance of wormhole routing algorithms. We show that in any network in which each physical channel, i.e., communication link, can support up to B virtual channels, it is possible to route any set of messages with L flits each, whose paths have congestion C and dilation D in (L + D)C(D log D) 1=B 2 O(log (C=D)) =B flit steps, where a flit step is the time taken to transmit a single flit across a link. We also prove a nearly matching lower bound, i.e., for any values of C, D, B, and L, where C; D B + 1 and L = (1 +\Omega\Gamma302 D, we show how to construct a network and a set of Lflit messages whose paths have congestion C and dilation D that require\Omega\Gamma LCD 1=B =B) flit steps to route. These upper and lower bounds imply that increasing the buffering capacity and the bandwidth of each physical channel by a factor of B can speed up a wormhole routing algorithm by a superlinear factor, i.e., a factor signi...
The effects of faults on network expansion
 In Proc. 16th ACM Symposium on Parallel Algorithms and Architectures
, 2004
"... We study the problem of how resilient networks are to node faults. Specifically, we investigate the question of how many faults a network can sustain and still contain a large (i.e., linearsized) connected component with approximately the same expansion as the original faultfree network. We use a ..."
Abstract

Cited by 9 (1 self)
 Add to MetaCart
(Show Context)
We study the problem of how resilient networks are to node faults. Specifically, we investigate the question of how many faults a network can sustain and still contain a large (i.e., linearsized) connected component with approximately the same expansion as the original faultfree network. We use a pruning technique that culls away those parts of the faulty network that have poor expansion. The faults may occur at random or be caused by an adversary. Our techniques apply in either case. In the adversarial setting, we prove that for every network with expansion α, a large connected component with basically the same expansion as the original network exists for up to a constant times α · n faults. We show this result is tight in the sense that every graph G of size n and uniform expansion α(·) can be broken into components of size o(n) with ω(α(n) · n) faults. Unlike the adversarial case, the expansion of a graph gives a very weak bound on its resilience to random faults. While it is the case, as before, that there are networks of uniform expansion Ω(1 / log n) that are not resilient against a fault probability of a constant times 1 / log n, it is also observed that there are networks of uniform expansion O(1 / √ n) that are resilient against a constant fault probability. Thus, we introduce a different parameter, called the span of a graph, which gives us a more precise handle on the maximum fault probability. We use the span to show the first known results for the effect of random faults on the expansion of ddimensional meshes. 1