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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. ..."
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Cited by 325 (5 self)
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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 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 ..."
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Cited by 191 (21 self)
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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...
ChernoffHoeffding Bounds for Applications with Limited Independence
 SIAM Journal on Discrete Mathematics
, 1995
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A New Approach to Computing Optimal Schedules for the JobShop Scheduling Problem
 In Proc. of the 5th International IPCO Conference
, 1996
"... . From a computational point of view, the jobshop scheduling problem is one of the most notoriously intractable NPhard optimization problems. In spite of a great deal of substantive research, there are instances of even quite modest size for which it is beyond our current understanding to solv ..."
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Cited by 95 (0 self)
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. From a computational point of view, the jobshop scheduling problem is one of the most notoriously intractable NPhard optimization problems. In spite of a great deal of substantive research, there are instances of even quite modest size for which it is beyond our current understanding to solve to optimality. We propose several new lower bounding procedures for this problem, and show how to incorporate them into a branchandbound procedure. Unlike almost all of the work done on this problem in the past thirty years, our enumerative procedure is not based on the disjunctive graph formulation, but is rather a timeoriented branching scheme. We show that our approach can solve most of the standard benchmark instances, and obtains the best known lower bounds on each. 1 Introduction In the jobshop scheduling problem we are given a set of n jobs, J , a set of m machines, M, and a set of operations, O. Each job consists of a chain of operations, let O j be the chain of operati...
Improved Approximation Algorithms for Shop Scheduling Problems
, 1994
"... In the job shop scheduling problem we are given m machines and n jobs; a job consists of a sequence of operations, each of which must be processed on a specified machine; the objective is to complete all jobs as quickly as possible. This problem is strongly NPhard even for very restrictive special ..."
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Cited by 90 (7 self)
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In the job shop scheduling problem we are given m machines and n jobs; a job consists of a sequence of operations, each of which must be processed on a specified machine; the objective is to complete all jobs as quickly as possible. This problem is strongly NPhard even for very restrictive special cases. We give the first randomized and deterministic polynomialtime algorithms that yield polylogarithmic approximations to the optimal length schedule. Our algorithms also extend to the more general case where a job is given not by a linear ordering of the machines on which it must be processed but by an arbitrary partial order. Comparable bounds can also be obtained when there are m 0 types of machines, a specified number of machines of each type, and each operation must be processed on one of the machines of a specified type, as well as for the problem of scheduling unrelated parallel machines subject to chain precedence constraints. Key Words: scheduling, approximation algorithms AM...
A Case Study of Multiservice, Multipriority Traffic Engineering Design for Data Networks
 Proc. IEEE Int’l Global Telecomm. Conf. (GLOBECOM ’99
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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 ..."
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Cited by 46 (5 self)
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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...
Preventing Traffic Analysis for RealTime Communication Networks
 Proceedings of The IEEE Military Communication Conference (MILCOM) '99
, 1999
"... AbstractIn this paper, we address issues related to preventing traffic analysis in computer networks used for realtime missioncritical applications. We consider an IPbased network where headers of packets, including source host address and destination host address, are readable by an observer (i. ..."
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AbstractIn this paper, we address issues related to preventing traffic analysis in computer networks used for realtime missioncritical applications. We consider an IPbased network where headers of packets, including source host address and destination host address, are readable by an observer (i.e., by a potential enemy). Although the encryption of network packets significantly increases privacy, the density of the traffic can still provide useful information to the observer. We take an approach by manipulating traffic in the network through hostbased rerouting and traffic padding so that the traffic shows a timeinvariant pattern. Thus, the observer can not derive any useful information about the real traffic pattern. By evaluating the performance of the algorithms used for this problem in terms of acceptance rate and execution time, we found that some wellknown theoretical optimal and nearoptimal algorithms failed to meet one or the other criteria. In this paper, we present a heuristic method that can effectively prevent traffic analysis while at the same time meeting realtime requirements. Our algorithm generates a plan that specifies where and when the dummy packets should be transmitted and if and how the payload packets should be rerouted and can yield high acceptance rate with low execution time. The success of the algorithm stems from the fact that it explicitly takes into account of realtime requirements and properly balances the traffic over the links. I.
On the inapproximability of disjoint paths and minimum steiner forest with bandwidth constraints
 Journal of Computer and Systems Sciences
"... In this paper, we study the inapproximability of several wellknown optimization problems in network optimization. We showthat the max directed vertexdisjoint paths problem cannot be approximated within ratio 2 log1& = n unless NP DTIME[2 polylog n], the max directed edgedisjoint paths proble ..."
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Cited by 14 (1 self)
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In this paper, we study the inapproximability of several wellknown optimization problems in network optimization. We showthat the max directed vertexdisjoint paths problem cannot be approximated within ratio 2 log1& = n unless NP DTIME[2 polylog n], the max directed edgedisjoint paths problem cannot be approximated within ratio 2 log1& = n unless NP DTIME [2 polylog n], the integer multicommodity flow problem in directed graphs cannot be approximated within ratio 2 log1& = n unless NP DTIME[2 polylog n], the max undirected vertexdisjoint paths problem does not have a polynomial time approximation scheme unless P=NP, and the minimum Steiner forest with bandwidth constraints problem cannot be approximated within ratio exp ( poly(n)) unless P=NP. 2000 Academic Press 1.
Improved Interior Point Algorithms for Exact and Approximate solution of Multicommodity Flow Problems
 In Proc. 6th ACMSIAM Symposium on Discrete Algorithms
, 1995
"... In this paper, we present a new interiorpoint based polynomial algorithm for the multicommodity flow problem and its variants. Unlike all previously known interior point algorithms for multicommodity flow that have the same complexity for approximate and exact solutions, our algorithm improves runn ..."
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Cited by 14 (1 self)
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In this paper, we present a new interiorpoint based polynomial algorithm for the multicommodity flow problem and its variants. Unlike all previously known interior point algorithms for multicommodity flow that have the same complexity for approximate and exact solutions, our algorithm improves running time in the approximate case by a polynomial factor. For many cases, the exact bounds are better as well. Instead of using the conventional linear programming formulation for the multicommodity flow problem, we model it as a quadratic optimization problem which is solved using interiorpoint techniques. This formulation allows us to exploit the underlying structure of the problem and to solve it efficiently. The algorithm is also shown to have improved stability properties. The improved complexity results extend to minimum cost multicommodity flow, concurrent flow and generalized flow problems. 1 Introduction The multicommodity flow problem is the problem of finding several network flo...