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Title:

Approximating Fractional Multicommodity Flow Independent of the Number of Commodities

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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 ...

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

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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:

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

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-03-22

Source:

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

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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:

A Fast Approximation Scheme for Fractional Covering Problems with Box Constraints

Description:

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

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Document Type:

text

Language:

en

DDC:

518 Numerical analysis *(computed)*

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Title:

Quickest flows over time

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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:

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

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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 tim...

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(|E| log |V|). We also present a variant of our algorithm that has O(|E| log |V|) worst-case complexity. Minimize

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The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2014-01-07

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

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Title:

Simple sybil-proof mechanisms for multi-level marketing. www.cs.dartmouth.edu/ druckerf/papers/sybil-abstract.pdf

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Multi-level marketing refers to a marketing approach in which buyers are encouraged to take an active role in promoting the product. This is done by offering them a reward for each successful referral of the product to other prospective buyers. To encourage potential customers to buy early and to give referrals to influential people, these mecha...

Multi-level marketing refers to a marketing approach in which buyers are encouraged to take an active role in promoting the product. This is done by offering them a reward for each successful referral of the product to other prospective buyers. To encourage potential customers to buy early and to give referrals to influential people, these mechanisms also reward indirect referrals — a direct referral linked to the buyer through other direct referrals. Doing so can make the referral/reward system vulnerable to sybil attacks — where profit maximizers create several replicas in order to maximize their rewards. In this paper we propose a family of mechanisms for which sybil attacks are not profitable. We do this by modifyinganymechanism thatsatisfiescertain natural properties of sensiblereward mechanismsto obtain one that is invulnerable to sybil attacks by profit maximizers while preserving its natural properties. Our modified mechanisms are also collusion proof. Finally, we give a concrete example of a natural mechanism that is sybil proof and simple to implement. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2013-07-19

Source:

http://www.cs.dartmouth.edu/~lkf/papers/fabio-ec12.pdf

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Document Type:

text

Language:

en

Subjects:

Categories and Subject Descriptors ; J.4 [Social and Behavioral Sciences ; Economics ; G.2.2 [Discrete Mathematics ; Graph Theory—Network problems General Terms ; Algorithms ; Economics Additional Key Words and Phrases ; Mechanism design ; Recommender systems ; Social networks

Categories and Subject Descriptors ; J.4 [Social and Behavioral Sciences ; Economics ; G.2.2 [Discrete Mathematics ; Graph Theory—Network problems General Terms ; Algorithms ; Economics Additional Key Words and Phrases ; Mechanism design ; Recommender systems ; Social networks Minimize

DDC:

303 Social processes *(computed)*

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Title:

On Identifying Strongly Connected Components in Parallel

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

. The standard serial algorithm for strongly connected components is based on depth first search, which is difficult to parallelize. We describe a divide-and-conquer algorithm for this problem which has significantly 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 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 applications in compiler analysis, data mining, scientific computing and other areas. The definitive serial algorithm for identifying strongly connected components is due to Tarjan [15] and is built on a depth first search of the graph. For a grap. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-04-13

Source:

http://www.cse.uiuc.edu/~alipinar/papers/irreg00.ps

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Document Type:

text

Language:

en

DDC:

511 General principles of mathematics *(computed)*

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Title:

Fast and Simple Approximation Schemes for Generalized Flow

Description:

We present fast and simple fully polynomial-time approximation schemes (FPTAS) for generalized versions of maximum flow, multicommodity flow, minimum cost maximum flow, and minimum cost multicommodity flow. We extend and refine fractional packing frameworks introduced in FPTAS's for traditional multicommodity flow and packing linear programs. Ou...

We present fast and simple fully polynomial-time approximation schemes (FPTAS) for generalized versions of maximum flow, multicommodity flow, minimum cost maximum flow, and minimum cost multicommodity flow. We extend and refine fractional packing frameworks introduced in FPTAS's for traditional multicommodity flow and packing linear programs. Our FPTAS's dominate the previous best known complexity bounds for all of these problems, some by more than a factor of n2, where n is the number of nodes. This is accomplished in part by introducing an efficient method of solving a sequence of generalized shortest path problems. Our generalized multicommodity FPTAS's are now as fast as the best non-generalized ones. We believe our improvements make it practical to solve generalized multicommodity flow problems via combinatorial methods. Minimize

Contributors:

The Pennsylvania State University CiteSeerX Archives

Year of Publication:

2009-01-19

Source:

http://www.cs.dartmouth.edu/~lkf/papers/packing5.ps.gz

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en

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