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Title:

Approximating fractional multicommodity flow independent of the number of commodities

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Abstract. 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 ...

Abstract. 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, running in O ∗ (ɛ −2 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 Könemann in FOCS 1998. They are simple, deterministic, and for the versions without costs, they are strongly polynomial. The approximation guarantees are obtained by comparison with dual feasible solutions found by our algorithm. 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 the maximum weight of a commodity. Key words. multicommodity flow, approximation algorithm, concurrent flow, VLSI routing Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-03-22

Source:

http://www.cs.dartmouth.edu/~lkf/papers/lpmulti.pdf

http://www.cs.dartmouth.edu/~lkf/papers/lpmulti.pdf Minimize

Document Type:

text

Language:

en

DDC:

518 Numerical analysis *(computed)*

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Title:

A Fast Approximation Scheme for Fractional Covering Problems with Box Constraints

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We present the first combinatorial approximation scheme that yields a pure approximation guarantee for linear programs that are either covering problems with upper bounds on variables, or their duals. Existing approximation schemes for mixed covering and packing problems do not simultaneously satisfy packing and covering constraints exactly. We ...

We present the first combinatorial approximation scheme that yields a pure approximation guarantee for linear programs that are either covering problems with upper bounds on variables, or their duals. Existing approximation schemes for mixed covering and packing problems do not simultaneously satisfy packing and covering constraints exactly. We present the first combinatorial approximation scheme that returns solutions that simultaneously satisfy general positive covering constraints and upper bounds on variable values. For input parameter ffl? 0, the returned solution has positive linear objective function value at most 1 + ffl times the optimal value. The general algorithm requires O(ffl2m log(cTu)) iterations, where c is the objective cost vector, u is the vector of upper bound values, and m is the number of variables. Each iteration uses an oracle that finds an (approximately) most violated constraint. A natural set of problems that our work addresses are linear programs for various network design problems: generalized Steiner network, vertex connectivity, directed connectivity, capacitated network design, group Steiner forest. The integer versions of these problems are all NP-hard. For each of them, there is an approximation algorithm that rounds the solution to the corresponding linear program relaxation. If the LP solution is not feasible, then the corresponding integer solution will also not be feasible. Solving the linear program is often the computational bottleneck in these problems, and thus a fast approximation scheme for the LP relaxation means faster approximation algorithms. For these applications, we introduce a new modification of the push-relabel maximum flow algorithm that allows us to perform each iteration in amortized O(jEj+jV j log jV j) time, instead of one maximum flow per iteration that is implied by the straight forward adaptation of our general algorithm. In conjunction with an observation that reduces the number of iterations to jEj log jV j for f0; 1g constraint matrices, the modification allows us to obtain an algorithm that is faster than existing exact or approximate algorithms by a factor of at least O(jEj) and by a factor of O(jEj log jV j) if the number of demand pairs is \Omega (jV j). Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-01-19

Source:

http://www.cs.dartmouth.edu/~lkf/papers/lp-journal.ps.gz

http://www.cs.dartmouth.edu/~lkf/papers/lp-journal.ps.gz Minimize

Document Type:

text

Language:

en

DDC:

518 Numerical analysis *(computed)*

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Metadata may be used without restrictions as long as the oai identifier remains attached to it.

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Title:

Approximating Fractional Multicommodity Flow Independent of the Number of Commodities

Description:

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 ...

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 . Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-13

Source:

http://www.ieor.columbia.edu/~lisa/papers/multi5.ps

http://www.ieor.columbia.edu/~lisa/papers/multi5.ps Minimize

Document Type:

text

Language:

en

DDC:

518 Numerical analysis *(computed)*

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Title:

Quickest flows over time

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Description:

LIMITED DISTRIBUTION NOTICE: This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. It has been issued as a Research

LIMITED DISTRIBUTION NOTICE: This report has been submitted for publication outside of IBM and will probably be copyrighted if accepted for publication. It has been issued as a Research Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-01-06

Source:

http://domino.watson.ibm.com/library/cyberdig.nsf/papers/49E00CD15329768985256D5D00516387/$File/RC22833.pdf

http://domino.watson.ibm.com/library/cyberdig.nsf/papers/49E00CD15329768985256D5D00516387/$File/RC22833.pdf Minimize

Document Type:

text

Language:

en

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Title:

Polynomial-time separation of a superclass of simple comb inequalities

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Abstract The comb inequalities are a well-known class of facet-inducing inequalities for the Traveling Salesman Problem, defined in terms of certain vertex sets called the handle and the teeth. We say that a comb inequality is simple if the following holds for each tooth: either the intersection of the tooth with the handle has cardinality one, ...

Abstract The comb inequalities are a well-known class of facet-inducing inequalities for the Traveling Salesman Problem, defined in terms of certain vertex sets called the handle and the teeth. We say that a comb inequality is simple if the following holds for each tooth: either the intersection of the tooth with the handle has cardinality one, or the part of the tooth outside the handle has cardinality one, or both. The simple comb inequalities generalize the classical 2-matching inequalities of Edmonds, and also the so-called Chv'atal comb inequalities. In 1982, Padberg and Rao [30] gave a polynomial-time separation algorithm for the 2-matching inequalities-- i.e., an algorithm for testing if a given fractional solution to an LP relaxation violates a 2-matching inequality. We extend this significantly by giving a polynomial-time separation algorithm for a class of valid inequalities which includes all simple comb inequalities. Key Words: traveling salesman problem, cutting planes, separation. 1 Introduction The famous Symmetric Traveling Salesman Problem (STSP) is the N P-hardproblem of finding a minimum cost Hamiltonian cycle (or tour) in a complete undirected graph. The most successful optimization algorithms at present (e.g. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-01-08

Source:

http://www.cs.dartmouth.edu/~lkf/papers/simpleDPfinal.ps.gz

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Document Type:

text

Language:

en

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Title:

On identifying strongly connected components in parallel

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Abstract. The standard serial algorithm for strongly connected components is based on depth rst search, which is di cult to parallelize. We describe a divide-and-conquer algorithm for this problem which has signi cantly greater potential for parallelization. For a graph with n vertices in which degrees are bounded by a constant, we show the expe...

Abstract. The standard serial algorithm for strongly connected components is based on depth rst search, which is di cult to parallelize. We describe a divide-and-conquer algorithm for this problem which has signi cantly greater potential for parallelization. For a graph with n vertices in which degrees are bounded by a constant, we show the expected serial running time of our algorithm to be O(n log n). 1 Minimize

Publisher:

Springer Verlag

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2008-07-17

Source:

http://ipdps.cc.gatech.edu/2000/irreg/18000506.pdf

http://ipdps.cc.gatech.edu/2000/irreg/18000506.pdf Minimize

Document Type:

text

Language:

en

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Title:

A Divide-And-Conquer Algorithm For Identifying Strongly Connected Components

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. The standard serial algorithm for strongly connected components has linear complexity and is based on depth first search. Unfortunately, depth first search is difficult to parallelize. We describe a divide--and--conquer algorithm for this problem which has significantly greater potential for parallelization. We show the expected serial running...

. The standard serial algorithm for strongly connected components has linear complexity and is based on depth first search. Unfortunately, depth first search is difficult to parallelize. We describe a divide--and--conquer algorithm for this problem which has significantly greater potential for parallelization. We show the expected serial running time of our algorithm to be O(jEj log jV j). We also present a variant of our algorithm that has O(jEj log jV j) worst--case complexity. Key words. Strongly connected components, divide--and--conquer, parallel algorithm, discrete ordinates method AMS subject classifications. 05C85, 05C38, 68W10, 68W20 1. Introduction. A strongly connected component of a directed graph is a maximal subset of vertices containing a directed path from each vertex to all others in the subset. The vertices of any directed graph can be partitioned into a set of disjoint strongly connected components. This decomposition is a fundamental tool in graph theory with app. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-15

Source:

ftp://ftp.cs.sandia.gov/pub/papers/bahendr/scc_theory.ps.gz

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Document Type:

text

Language:

en

Subjects:

ordinates

ordinates Minimize

DDC:

511 General principles of mathematics *(computed)*

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Title:

Optimal Rounding of Instantaneous Fractional Flows Over Time

Description:

A transshipment problem with demands that exceed network capacity can be solved by sending flow in several waves. How can this be done in the minimum number, T, of waves, and at minimum cost, if costs are piece-wise linear convex functions of the flow? In this paper, we show that this problem can be solved using min{m,logT, l+og(mu)-g(U)} maximu...

A transshipment problem with demands that exceed network capacity can be solved by sending flow in several waves. How can this be done in the minimum number, T, of waves, and at minimum cost, if costs are piece-wise linear convex functions of the flow? In this paper, we show that this problem can be solved using min{m,logT, l+og(mu)-g(U)} maximum flow computations and one minimum (convex) cost flow computation. Here m is the number of arcs, F is the maximum supply or demand, and U is the maximum capacity. When there is only one sink, this problem can be solved in the same asymptotic time as one minimum (convex) cost flow computation. This improves upon the recent algorithm in [5] which solves the quickest transshipment problem (the above mentioned problem without costs) on k terminals using k logT maximum flow computations and k minimum cost flow computations. Our solutions start with a stationary fractional flow, as described in [5], and use rounding to transform this into an integral flow. The rounding procedure takes O(n) time. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2011-08-03

Source:

http://dspace.mit.edu/bitstream/1721.1/5118/1/OR-340-99-46439172.pdf

http://dspace.mit.edu/bitstream/1721.1/5118/1/OR-340-99-46439172.pdf Minimize

Document Type:

text

Language:

en

DDC:

532 Fluid mechanics; liquid mechanics *(computed)*

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Title:

Approximately Optimal control of Fluid Networks

Description:

We give an approximation algorithm for the optimal control problem in fluid networks. Such problems arise as fluid relaxations of multiclass queueing networks, and are used to find approximate solutions to complex job shop scheduling problems. In a network with linear flow costs and linear, per-unit-time holding costs, our algorithm finds a drai...

We give an approximation algorithm for the optimal control problem in fluid networks. Such problems arise as fluid relaxations of multiclass queueing networks, and are used to find approximate solutions to complex job shop scheduling problems. In a network with linear flow costs and linear, per-unit-time holding costs, our algorithm finds a drainage of the network, that for given constants ε>0andδ>0 has total cost (1 + ε)OPT + δ, whereOPT is the cost of the minimum cost drainage. The complexity of our algorithm is polynomial in the size of the input network, 1/ε, and log 1. The fluid relaxation is a continuous problem. While the problem is known to have a δ piecewise constant solution, it is not known to have a polynomially-sized solution. We introduce a natural discretization of polynomial size and prove that this discretization produces a solution with low cost. This is the first polynomial time algorithm with a provable approximation guarantee for fluid relaxations. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-06-17

Source:

http://domino.watson.ibm.com/library/cyberdig.nsf/papers/50C56EA0EBA6DC3685256D5D0065DD4C/$File/RC22834.pdf

http://domino.watson.ibm.com/library/cyberdig.nsf/papers/50C56EA0EBA6DC3685256D5D0065DD4C/$File/RC22834.pdf Minimize

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text

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en

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Title:

Optimal Rounding of Instantaneous Fractional Flows Over Time

Description:

A transshipment problem with demands that exceed network capacity can be solved by sending flow in several waves. How can this be done in the minimum number, T, of waves, and at minimum cost, if costs are piecewise linear convex functions of the flow? In this paper, we show that this problem can be solved using $\min\{ m,\log T,\ub{\Gamma}{U} \}...

A transshipment problem with demands that exceed network capacity can be solved by sending flow in several waves. How can this be done in the minimum number, T, of waves, and at minimum cost, if costs are piecewise linear convex functions of the flow? In this paper, we show that this problem can be solved using $\min\{ m,\log T,\ub{\Gamma}{U} \}$ maximum flow computations and one minimum (convex) cost flow computation. Here m is the number of arcs, $\Gamma$ is the maximum supply or demand, and U is the maximum capacity. When there is only one sink, this problem can be solved in the same asymptotic time as one minimum (convex) cost flow computation. This improves upon the previous best algorithm to solve the problem without costs by a factor of k. Our solutions start with a stationary fractional flow and use rounding to transform this into an integral flow. The rounding procedure takes O(n) time. Minimize

Publisher:

Society for Industrial and Applied Mathematics

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-07-31

Source:

http://web.mit.edu/jorlin/www/papersfolder/Rounding_Flows.pdf

http://web.mit.edu/jorlin/www/papersfolder/Rounding_Flows.pdf Minimize

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text

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en

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