Results 1  10
of
29
Faster and simpler algorithms for multicommodity flow and other fractional packing problems
"... This paper considers the problem of designing fast, approximate, combinatorial algorithms for multicommodity flows and other fractional packing problems. We present new faster and much simpler algorithms for these problems. ..."
Abstract

Cited by 270 (5 self)
 Add to MetaCart
This paper considers the problem of designing fast, approximate, combinatorial algorithms for multicommodity flows and other fractional packing problems. We present new faster and much simpler algorithms for these problems.
Fast Approximation Algorithms for Fractional Packing and Covering Problems
, 1995
"... This paper presents fast algorithms that find approximate solutions for a general class of problems, which we call fractional packing and covering problems. The only previously known algorithms for solving these problems are based on general linear programming techniques. The techniques developed ..."
Abstract

Cited by 232 (13 self)
 Add to MetaCart
This paper presents fast algorithms that find approximate solutions for a general class of problems, which we call fractional packing and covering problems. The only previously known algorithms for solving these problems are based on general linear programming techniques. The techniques developed in this paper greatly outperform the general methods in many applications, and are extensions of a method previously applied to find approximate solutions to multicommodity flow problems. Our algorithm is a Lagrangean relaxation technique; an important aspect of our results is that we obtain a theoretical analysis of the running time of a Lagrangean relaxationbased algorithm. We give several applications of our algorithms. The new approach yields several orders of magnitude of improvement over the best previously known running times for algorithms for the scheduling of unrelated parallel machines in both the preemptive and the nonpreemptive models, for the job shop problem, for th...
Fast Approximation Algorithms for Multicommodity Flow Problems
 JOURNAL OF COMPUTER AND SYSTEM SCIENCES
, 1991
"... All previously known algorithms for solving the multicommodity flow problem with capacities are based on linear programming. The best of these algorithms [15] uses a fast matrix multiplication algorithm and takes O(k 3:5 n 3 m :5 log(nDU )) time for the multicommodity flow problem with inte ..."
Abstract

Cited by 170 (20 self)
 Add to MetaCart
All previously known algorithms for solving the multicommodity flow problem with capacities are based on linear programming. The best of these algorithms [15] uses a fast matrix multiplication algorithm and takes O(k 3:5 n 3 m :5 log(nDU )) time for the multicommodity flow problem with integer demands and at least O(k 2:5 n 2 m :5 log(nffl \Gamma1 DU )) time to find an approximate solution, where k is the number of commodities, n and m denote the number of nodes and edges in the network, D is the largest demand, and U is the largest edge capacity. Substantially more time is needed to find an exact solution. As a consequence, even multicommodity flow problems with just a few commodities are believed to be much harder than singlecommodity maximumflow or minimumcost flow problems. In this paper, we describe the first polynomialtime combinatorial algorithms for approximately solving the multicommodity flow problem. The running time of our randomized algorithm i...
Faster approximation algorithms for the unit capacity concurrent flow problem with applications to routing and finding sparse cuts
 SIAM Journal on Computing
, 1994
"... Abstract. This paper describes new algorithms for approximately solving the concurrent multicommodity flow problem with uniform capacities. These algorithms are much faster than algorithms discovered previously. Besides being an important problem in its own right, the uniformcapacity concurrent flo ..."
Abstract

Cited by 84 (20 self)
 Add to MetaCart
Abstract. This paper describes new algorithms for approximately solving the concurrent multicommodity flow problem with uniform capacities. These algorithms are much faster than algorithms discovered previously. Besides being an important problem in its own right, the uniformcapacity concurrent flow problem has many interesting applications. Leighton and Rao used uniformcapacity concurrent flow to find an approximately "sparsest cut " in a graph and thereby approximately solve a wide variety of graph problems, including minimum feedback arc set, minimum cut linear arrangement, and minimum area layout. However, their method appeared to be impractical as it required solving a large linear program. This paper shows that their method might be practical by giving an O(m log m) expectedtime randomized algorithm for their concurrent flow problem on an medge graph. Raghavan and Thompson used uniformcapacity concurrent flow to solve approximately a channel width minimization problem in very large scale integration. An O (k 3/2 (m + n log n)) expectedtime randomized algorithm and an O (k min {n, k} (m + n log n) log k) deterministic algorithm is given for this problem when the channel width is f2 (log n), where k denotes the number of wires to be routed in an nnode, medge network. Key words, multicommodity flow, approximation, concurrent flow, graph separators, VLSI routing AMS subject classification. 68Q25, 90C08, 90C27 1. Introduction. The
A Simple LocalControl Approximation Algorithm for Multicommodity Flow
 In Proceedings of the 34th Annual Symposium on Foundations of Computer Science
, 1993
"... In this paper, we describe a very simple (1 + ") approximation algorithm for the multicommodity flow problem. The algorithm runs in time that is polynomial in N (the number of nodes in the network) and ffl \Gamma1 (the closeness of the approximation to optimal). The algorithm is remarkable in th ..."
Abstract

Cited by 65 (6 self)
 Add to MetaCart
In this paper, we describe a very simple (1 + ") approximation algorithm for the multicommodity flow problem. The algorithm runs in time that is polynomial in N (the number of nodes in the network) and ffl \Gamma1 (the closeness of the approximation to optimal). The algorithm is remarkable in that it is much simpler than all known polynomial time flow algorithms (including algorithms for the special case of onecommodity flow). In particular, the algorithm does not rely on augmenting paths, shortest paths, mincost paths, or similar techniques to push flow through a network. In fact, no explicit attempt is ever made to push flow towards a sink during the algorithm. Because the algorithm is so simple, it can be applied to a variety of problems for which centralized decision making and flow planning is not possible. For example, the algorithm can be easily implemented with local control in a distributed network and it can be made tolerant to link failures. In addition, the algorithm ...
Adding Multiple Cost Constraints to Combinatorial Optimization Problems, with Applications to Multicommodity Flows
 IN PROCEEDINGS OF THE 27TH ANNUAL ACM SYMPOSIUM ON THEORY OF COMPUTING
, 1995
"... Minimum cost multicommodity flow is an instance of a simpler problem (multicommodity flow) to which a cost constraint has been added. In this paper we present a general scheme for solving a large class of such "costadded" problemseven if more than one cost is added. One of the main applicatio ..."
Abstract

Cited by 45 (5 self)
 Add to MetaCart
Minimum cost multicommodity flow is an instance of a simpler problem (multicommodity flow) to which a cost constraint has been added. In this paper we present a general scheme for solving a large class of such "costadded" problemseven if more than one cost is added. One of the main applications of this method is a new deterministic algorithm for approximately solving the minimumcost multicommodity flow problem. Our algorithm finds a (1 + ffl) approximation to the minimum cost flow in ~ O(ffl \Gamma3 kmn) time, where k is the number of commodities, m is the number of edges, and n is the number vertices in the input problem. This improves the previous best deterministic bounds of O(ffl \Gamma4 kmn 2 ) [9] and ~ O(ffl \Gamma2 k 2 m 2 ) [15] by factors of n=ffl and fflkm=n respectively. In fact, it even dominates the best randomized bound of ~ O(ffl \Gamma2 km 2 ) [15]. The algorithm presented in this paper efficiently solves several other interesting generali...
Combinatorial Algorithms for the Generalized Circulation Problem
 MATHEMATICS OF OPERATIONS RESEARCH
, 1989
"... We consider a generalization of the maximum flow problem in which the amounts of flow entering and leaving an arc are linearly related. More precisely, if x(e) units of flow enter an arc e, x(e)fl(e) units arrive at the other end. For instance, nodes of the graph can correspond to different curre ..."
Abstract

Cited by 26 (3 self)
 Add to MetaCart
We consider a generalization of the maximum flow problem in which the amounts of flow entering and leaving an arc are linearly related. More precisely, if x(e) units of flow enter an arc e, x(e)fl(e) units arrive at the other end. For instance, nodes of the graph can correspond to different currencies, with the multipliers being the exchange rates. We require conservation of flow at every node except a given source node. The goal is to maximize the amount of flow excess at the source. This problem is a special case of linear programming, and therefore can be solved in polynomial time. In this paper we present the first polynomial time combinatorial algorithms for this problem. The algorithms are simple and intuitive.
An Implementation of a Combinatorial Approximation Algorithm for MinimumCost Multicommodity Flow
, 1997
"... The minimumcost multicommodity flow problem involves simultaneously shipping multiple commodities through a single network so that the total flow obeys arc capacity constraints and has minimum cost. ..."
Abstract

Cited by 23 (3 self)
 Add to MetaCart
The minimumcost multicommodity flow problem involves simultaneously shipping multiple commodities through a single network so that the total flow obeys arc capacity constraints and has minimum cost.