In this paper, we establish max-flow min-cut theorems for several important classes of multicommodity flow problems. In particular, we show that for any n-node multicommodity flow problem with uniform demands, the max...
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In this paper, we establish max-flow min-cut theorems for several important classes of multicommodity flow problems. In particular, we show that for any n-node multicommodity flow problem with uniform demands, the max-flow for the problem is within an O(log n) factor of the upper bound implied by the min-cut. The result (which is existentially optimal) establishes an important analogue of the famous I-commodity max-now min-cut 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 polynomial-time (polylog n-times-optimal) approximation algorithms for well-known NP-hard optimization problems such as graph partitioning, min-cut linear arrangement, crossing number, VLSI layout, and minimum feedback are 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.
We present a polynomial-time Markov chain Monte Carlo algorithm for estimating the partition function of the antiferromagnetic Ising model on any line graph. The analysis of the algorithm exploits the 'winding'...
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We present a polynomial-time Markov chain Monte Carlo algorithm for estimating the partition function of the antiferromagnetic Ising model on any line graph. The analysis of the algorithm exploits the 'winding' technology devised by McQuillan [CoRR abs/1301.2880 (2013)] and developed by Huang, Lu and Zhang [Proc. 27th Symp. on Disc. algorithms (SODA16), 514-527]. We show that exact computation of the partition function is #P-hard, even for line graphs, indicating that an approximation algorithm is the best that can be expected. We also show that Glauber dynamics for the Ising model is rapidly mixing on line graphs, an example being the kagome lattice.
approximation algorithms for embedding hyperedges in a cycle so as to minimize the maximum congestion are presented. Our algorithms generate an embedding by transforming the problem into another problem solvable in po...
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approximation algorithms for embedding hyperedges in a cycle so as to minimize the maximum congestion are presented. Our algorithms generate an embedding by transforming the problem into another problem solvable in polynomial time. One algorithm transforms it to a linear programming problem, and the other one to the problem of embedding edges in a cycle. Both algorithms generate an embedding with congestion at most twice of that in an optimal solution. Our problem has applications in CAD and parallel computation. (C) 1998 Elsevier Science B.V. All rights reserved.
We study the approximability of instances of the minimum entropy set cover problem, parameterized by the average frequency of a random element in the covering sets. We analyze an algorithm combining a greedy approach ...
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We study the approximability of instances of the minimum entropy set cover problem, parameterized by the average frequency of a random element in the covering sets. We analyze an algorithm combining a greedy approach with another one biased towards large sets. The algorithm is controlled by the percentage of elements to which we apply the biased approach. The optimal parameter choice leads to improved approximation guarantees when average element frequency is less than e. (C) 2014 Elsevier B.V. All rights reserved.
The terminal Steiner tree problem is a special version of the Steiner tree problem, where a Steiner minimum tree has to be found in which all terminals are leaves. We prove that no polynomial time approximation algori...
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The terminal Steiner tree problem is a special version of the Steiner tree problem, where a Steiner minimum tree has to be found in which all terminals are leaves. We prove that no polynomial time approximation algorithm for the terminal Steiner tree problem can achieve an approximation ratio less than (I - o(l)) Inn unless NP has slightly superpolynomial time algorithms. Moreover, we present a polynomial time approximation algorithm for the metric version of this problem with a performance ratio of 2rho, where rho denotes the best known approximation ratio for the Steiner tree problem. This improves the previously best known approximation ratio for the metric terminal Steiner tree problem of rho + 2. (C) 2003 Elsevier B.V. All rights reserved.
The densest k-subgraph problem asks for a k-vertex subgraph with the maximum number of edges. This problem is NP-hard on bipartite graphs, chordal graphs, and planar graphs. A 3-approximation algorithm is known for ch...
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The densest k-subgraph problem asks for a k-vertex subgraph with the maximum number of edges. This problem is NP-hard on bipartite graphs, chordal graphs, and planar graphs. A 3-approximation algorithm is known for chordal graphs. We present 3/2-approximation algorithms for proper interval graphs and bipartite permutation graphs. The latter result relies on a new characterisation of bipartite permutation graphs which may be of independent interest. (C) 2010 Elsevier B.V. All rights reserved.
Arpe and Manthey [J. Arpe, B. Manthey, Approximability of minimum AND-circuits, Algorithmica 53 (3) (2009) 337-357] recently studied the minimum AND-circuit problem, which is a circuit minimization problem, and showed...
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Arpe and Manthey [J. Arpe, B. Manthey, Approximability of minimum AND-circuits, Algorithmica 53 (3) (2009) 337-357] recently studied the minimum AND-circuit problem, which is a circuit minimization problem, and showed some results including approximation algorithms, APX-hardness and fixed parameter tractability of the problem. In this note, we show that algorithms via the k-set cover problem yield improved approximation ratios for the minimum AND-circuit problem with maximum degree three. In particular, we obtain an approximation ratio of 1.199 for the problem with maximum degree three and unbounded multiplicity. (C) 2010 Elsevier B.V. All rights reserved.
A linear reinforcement learning technique is proposed to provide a memory and thus accelerate the convergence of successive approximation algorithms. The learning scheme is used to update weighting coefficients applie...
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A linear reinforcement learning technique is proposed to provide a memory and thus accelerate the convergence of successive approximation algorithms. The learning scheme is used to update weighting coefficients applied to the components of the correction terms of the algorithm. A direction of the search approaching the direction of a "ridge" will result in a gradient peak-seeking method which accelerates considerably the convergence to a neighborhood of the extremum. In a stochastic approximation algorithm the learning scheme provides the required memory to establish a consistent direction or search insensitive to perturbations introduced by the random variables involved. The accelerated algorithms and the respective proofs of convergence are presented. Illustrative examples demonstrate the validity of the proposed algorithms.
This article addresses the scheduling problem of coflows in identical parallel networks, a well-known NPNP-hard problem. We consider both flow-level scheduling and coflow-level scheduling problems. In the flow-level s...
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In this paper, we present a simple factor 6 algorithm for approximating the optimal multiplicative distortion of embedding a graph metric into a tree metric (thus improving and simplifying the factor 100 and 27 algori...
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In this paper, we present a simple factor 6 algorithm for approximating the optimal multiplicative distortion of embedding a graph metric into a tree metric (thus improving and simplifying the factor 100 and 27 algorithms of BCZdoiu et al. (Proceedings of the eighteenth annual ACM-SIAM symposium on discrete algorithms (SODA 2007), pp. 512-521, 2007) and BCZdoiu et al. (Proceedings of the 11th international workshop on approximation algorithms for combinatorial optimization problems (APPROX 2008), Springer, Berlin, pp. 21-34, 2008)). We also present a constant factor algorithm for approximating the optimal distortion of embedding a graph metric into an outerplanar metric. For this, we introduce a general notion of a metric relaxed minor and show that if G contains an alpha-metric relaxed H-minor, then the distortion of any embedding of G into any metric induced by a H-minor free graph is a parts per thousand yen alpha. Then, for H=K (2,3), we present an algorithm which either finds an alpha-relaxed minor, or produces an O(alpha)-embedding into an outerplanar metric.
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