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22
Multicommodity maxflow mincut theorems and their use in designing approximation algorithms
 J. ACM
, 1999
"... In this paper, we establish maxflow mincut theorems for several important classes of multicommodity flow problems. In particular, we show that for any nnode multicommodity flow problem with uniform demands, the maxflow for the problem is within an O(log n) factor of the upper bound implied by ..."
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Cited by 357 (6 self)
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In this paper, we establish maxflow mincut theorems for several important classes of multicommodity flow problems. In particular, we show that for any nnode multicommodity flow problem with uniform demands, the maxflow for the problem is within an O(log n) factor of the upper bound implied by the mincut. The result (which is existentially optimal) establishes an important analogue of the famous 1commodity maxflow mincut theorem for problems with multiple commodities. The result also has substantial applications to the field of approximation algorithms. For example, we use the flow result to design the first polynomialtime (polylog ntimesoptimal) approximation algorithms for wellknown NPhard optimization problems such as graph partitioning, mincut linear arrangement, crossing number, VLSI layout, and minimum feedback arc set. Applications of the flow results to path routing problems, network reconfiguration, communication in distributed networks, scientific computing and rapidly mixing Markov chains are also described in the paper.
Approximating Fractional Multicommodity Flow Independent of the Number of Commodities
, 1999
"... We describe fully polynomial time approximation schemes for various multicommodity flow problems in graphs with m edges and n vertices. We present the first approximation scheme for maximum multicommodity flow that is independent of the number of commodities k, and our algorithm improves upon the ru ..."
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Cited by 110 (8 self)
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We describe fully polynomial time approximation schemes for various multicommodity flow problems in graphs with m edges and n vertices. We present the first approximation scheme for maximum multicommodity flow that is independent of the number of commodities k, and our algorithm improves upon the runtime of previous algorithms by this factor of k, performing in O (ffl \Gamma2 m 2 ) time. For maximum concurrent flow, and minimum cost concurrent flow, we present algorithms that are faster than the current known algorithms when the graph is sparse or the number of commodities k is large, i.e. k ? m=n. Our algorithms build on the framework proposed by Garg and Konemann [4]. They are simple, deterministic, and for the versions without costs, they are strongly polynomial. Our maximum multicommodity flow algorithm extends to an approximation scheme for the maximum weighted multicommodity flow, which is faster than those implied by previous algorithms by a factor of k= log W where W is ...
A Cutting Plane Algorithm for Multicommodity Survivable Network Design Problems
, 1995
"... We present a cutting plane algorithm for solving the following network design problem in telecommunications: given pointtopointtraffic demandsinanetwork,specified survivabilityrequirementsanda discretecost/capacityfunctionforeachlink, find minimumcostcapacityexpansionssatisfyingthegiven demands. ..."
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Cited by 49 (0 self)
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We present a cutting plane algorithm for solving the following network design problem in telecommunications: given pointtopointtraffic demandsinanetwork,specified survivabilityrequirementsanda discretecost/capacityfunctionforeachlink, find minimumcostcapacityexpansionssatisfyingthegiven demands. The algorithm is based onthe polyhedralstudyintheaccompanying paper [16]. We describe the underlying problem,the model and the main ingredients in our algorithm: initial formulation,feasibility test, separation for strong cutting planes and primal heuristics. Computational results for a set of realworld problems are reported.
A Bundle Type DualAscent Approach to Linear Multicommodity MinCost Flow Problems
"... We present a Cost Decomposition approach for the linear Multicommodity MinCost Flow problem, where the mutual capacity constraints are dualized and the resulting Lagrangean Dual is solved with a dualascent algorithm belonging to the class of Bundle methods. Although decomposition approaches to bl ..."
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Cited by 36 (16 self)
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We present a Cost Decomposition approach for the linear Multicommodity MinCost Flow problem, where the mutual capacity constraints are dualized and the resulting Lagrangean Dual is solved with a dualascent algorithm belonging to the class of Bundle methods. Although decomposition approaches to blockstructured Linear Programs have been reported not to be competitive with generalpurpose software, our extensive computational comparison shows that, when carefully implemented, a decomposition algorithm can outperform several other approaches, especially on problems where the number of commodities is “large ” with respect to the size of the graph. Our specialized Bundle algorithm is characterized by a new heuristic for the trust region parameter handling, and embeds a specialized Quadratic Program solver that allows the efficient implementation of strategies for reducing the number of active Lagrangean variables. We also exploit the structural properties of the singlecommodity MinCost Flow subproblems to reduce the overall computational cost. The proposed approach can be easily extended to handle variants of the problem.
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. ..."
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Cited by 32 (3 self)
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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.
Computational Experience with a Difficult MixedInteger Multicommodity Flow Problem
 MATHEMATICAL PROGRAMMING
, 1994
"... The following problem arises in the study of lightwave networks. Given a demand matrix containing amounts to be routed between corresponding nodes, we wish to design a network with certain topological features, and in this network, route all the demands, so that the maximum load (total flow) on any ..."
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Cited by 29 (1 self)
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The following problem arises in the study of lightwave networks. Given a demand matrix containing amounts to be routed between corresponding nodes, we wish to design a network with certain topological features, and in this network, route all the demands, so that the maximum load (total flow) on any edge is minimized. As we show, even small instances of this combined design/routing problem are extremely intractable. We describe computational experience with a cutting plane algorithm for this problem.
Provably Good Global Buffering Using an Available Buffer Block Plan
 PLAN,” PROCEEDINGS OF THE IEEE/ACM INTERNATIONAL CONFERENCE ON COMPUTERAIDED DESIGN
, 2000
"... To implement highperformance global interconnect without impacting the performance of existing blocks, the use of buffer blocks is increasingly popular in structuredcustom and blockbased ASIC/SOC methodologies. Recent works by Cong et al. [6] and Tang and Wong [25] give algorithms to solve the bu ..."
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Cited by 27 (5 self)
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To implement highperformance global interconnect without impacting the performance of existing blocks, the use of buffer blocks is increasingly popular in structuredcustom and blockbased ASIC/SOC methodologies. Recent works by Cong et al. [6] and Tang and Wong [25] give algorithms to solve the buffer block planning problem. In this paper we address the problem of how to perform buffering of global nets given an existing buffer block plan. Assuming as in [6, 25] that global nets have been already decomposed into twopin connections, we give a provably good algorithm based on a recent approach of Garg and Könemann [8] and Fleischer [7]. Our method routes connections using available buffer blocks, such that required upper and lower bounds on buffer intervals – as well as wirelength upper bounds per connection – are satisfied. Unlike [6, 25], our model allows more than one buffer to be inserted into any given connection. In addition, our algorithm observes buffer parity constraints, i.e., it will choose to use an inverter or a buffer ( = colocated pair of inverters) according to source and destination signal parity. The algorithm outperforms previous approaches [6] and has been validated on toplevel layouts extracted from a recent highend microprocessor design.
Vehicle Scheduling in Public Transit and Lagrangean Pricing
 Management Sci
, 1998
"... This paper investigates the solution of the linear programming (LP) relaxation of the multicommodity flow formulation of the multipledepot vehicle scheduling problems arising in public mass transit. We develop a column generation technique that makes it possible to solve the huge linear programs th ..."
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Cited by 15 (0 self)
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This paper investigates the solution of the linear programming (LP) relaxation of the multicommodity flow formulation of the multipledepot vehicle scheduling problems arising in public mass transit. We develop a column generation technique that makes it possible to solve the huge linear programs that come up there. The technique, which we call Lagrangean pricing, is based on two different Lagrangean relaxations. We describe in detail the basic ingredients of our approach and give computational results for largescale test data (with up to 70 million variables) from three German public transportation companies. Because of these results, we propose Lagrangean pricing as one of the basic ingredients of an effective method to solve multipledepot vehicle scheduling problems to proven optimality.
Experiments With a Network Design Algorithm Using EpsilonApproximate Linear Programs
, 1998
"... We describe an upperbound algorithm for multicommodity network design problems that relies on new results for approximately solving certain linear programs, and on the greedy heuristic for setcovering problems. 1 Introduction. Network design problems are mixedinteger programs that have the fo ..."
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Cited by 8 (3 self)
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We describe an upperbound algorithm for multicommodity network design problems that relies on new results for approximately solving certain linear programs, and on the greedy heuristic for setcovering problems. 1 Introduction. Network design problems are mixedinteger programs that have the following broad structure. Given a graph, and a set of "demands"  positive amounts to be routed between pairs of vertices  capacity must be added to the edges and/or vertices of the graph, in discrete amounts, and at minimum cost, so that a feasible routing is possible. Problem of this form are increasingly important in telecommunications applications, because of the great expense inherent in maintaining and upgrading metropolitan networks. A wide variety of special cases have been studied. For example, one may be constrained to using a fixed family of paths to carry out the routing, or to using a single path for each demand, or to using integral flows. The precise manner in which capacit...
What Do We Learn from Experimental Algorithmics?
 In Mathematical Foundations of Computer Science
, 2000
"... Experimental Algorithmics is concerned with the design, implementation, tuning, debugging and performance analysis of computer programs for solving algorithmic problems. It provides methodologies and tools for designing, developing and experimentally analyzing efficient algorithmic codes and aim ..."
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Cited by 6 (0 self)
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Experimental Algorithmics is concerned with the design, implementation, tuning, debugging and performance analysis of computer programs for solving algorithmic problems. It provides methodologies and tools for designing, developing and experimentally analyzing efficient algorithmic codes and aims at integrating and reinforcing traditional theoretical approaches for the design and analysis of algorithms and data structures. In this paper we survey some relevant contributions to the field of Experimental Algorithmics and we discuss significant examples where the experimental approach helped in developing new ideas, in assessing heuristics and techniques, and in gaining a deeper insight about existing algorithms. 1