Mathematical research on multicriteria optimization problems predominantly revolves around the set of Pareto optimal solutions. In practice, on the other hand, methods that output a single solution are more widespread...
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Mathematical research on multicriteria optimization problems predominantly revolves around the set of Pareto optimal solutions. In practice, on the other hand, methods that output a single solution are more widespread. Reference point methods are a successful example of this approach and are widely used in real-world multicriteria optimization. A reference point solution is the solution closest to a given reference point in the objective space. We study the connection between reference point methods and approximation algorithms for multicriteria optimization problems over discrete sets. In particular, we establish that, in terms of computational complexity, computing approximate reference point solutions is polynomially equivalent to approximating the Pareto set. Complementing these results, we show for a number of general algorithmic techniques in single criteria optimization how they can be lifted to reference point optimization. In particular, we lift the link between dynamic programming and FPTAS, as well as certain LP-rounding techniques. The latter applies, e.g., to SET COVER and several machine scheduling problems. (C) 2016 Elsevier B.V. All rights reserved.
Let c, k be two positive integers. Given a graph , the c-Load Coloring problem asks whether there is a c-coloring such that for every , there are at least k edges with both endvertices colored i. Gutin and Jones (Inf ...
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Let c, k be two positive integers. Given a graph , the c-Load Coloring problem asks whether there is a c-coloring such that for every , there are at least k edges with both endvertices colored i. Gutin and Jones (Inf Process Lett 114:446-449, 2014) studied this problem with . They showed 2-Load Coloring to be fixed-parameter tractable (FPT) with parameter k by obtaining a kernel with at most 7k vertices. In this paper, we extend the study to any fixed c by giving both a linear-vertex and a linear-edge kernel. In the particular case of , we obtain a kernel with less than 4k vertices and less than edges. These results imply that for any fixed , c-Load Coloring is FPT and the optimization version of c-Load Coloring (where k is to be maximized) has an approximation algorithm with a constant ratio.
In this paper we show a new way of constructing deterministic polynomial-time approximation algorithms for computing complex-valued evaluations of a large class of graph polynomials on bounded degree graphs. In partic...
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In this paper we show a new way of constructing deterministic polynomial-time approximation algorithms for computing complex-valued evaluations of a large class of graph polynomials on bounded degree graphs. In particular, our approach works for the Tutte polynomial and independence polynomial, as well as partition functions of complex-valued spin and edge-coloring models. More speci fi cally, we de fi ne a large class of graph polynomials C and show that if p is an element of C and there is a disk D centered at zero in the complex plane such that p (G) does not vanish on D for all bounded degree graphs G, then for each z in the interior of D there exists a deterministic polynomialtime approximation algorithm for evaluating p (G) at z. This gives an explicit connection between absence of zeros of graph polynomials and the existence of e ffi cient approximation algorithms, allowing us to show new relationships between well-known conjectures. Our work builds on a recent line of work initiated by Barvinok [Found. Comput. Math., 16 (2016), pp. 329-342;Theory Comput., 11 (2015), pp. 339-355;Computing the Partition Function of a Polynomial on the Boolean Cube, 2015;Discrete Anal., 2 (2017), 34pp], which provides a new algorithmic approach besides the existing Markov chain Monte Carlo method and the correlation decay method for these types of problems.
In an earlier paper (Bao and Liu [1]), we considered a version of the clustered traveling salesman problem (CTSP), in which both the starting and ending vertex of each cluster are free to be selected, and proposed a 2...
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In an earlier paper (Bao and Liu [1]), we considered a version of the clustered traveling salesman problem (CTSP), in which both the starting and ending vertex of each cluster are free to be selected, and proposed a 2.167-approximation algorithm. In this note, we first improve this approximation ratio to 1.9 by introducing a new method to define the inter node lengths for all the nodes in Step 2 of Algorithm A of Bao and Liu [1]. Based on the above method, we then provide a 2,5-approximation algorithm for another version of CTSP where the starting vertex of each cluster is given while the ending vertex is free to be selected, which improves the previous approximation ratio of 2.643 of Guttmann-Beck et al. [5]. (C) 2017 Elsevier B.V. All rights reserved.
In the past decades, there has been a burst of activity to simplify implementation of complex software systems. The solution framework in software engineering community for this problem is called component-based softw...
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In the past decades, there has been a burst of activity to simplify implementation of complex software systems. The solution framework in software engineering community for this problem is called component-based software design (CBSD), whereas in the modeling and simulation community it is called composability. Composability is a complex feature due to the challenges of creating components, selecting combinations of components, and integrating the selected components. In this paper, we address the challenge through the analysis of Component Selection (CS), the NP-complete process of selecting a minimal set of components to satisfy a set of objectives. Due to the computational complexity of CS, we consider approximation algorithms that make the component selection process practical. We define three variations of CS and present good approximation algorithms to find near optimal solutions. In spite of our creation of approximable variants of Component Selection, we prove that the general Component Selection problem is inapproximable.
We evaluate the performance of fast approximation algorithms for MAX SAT on the comprehensive benchmark sets from the SAT and MAX SAT contests. Our examination of a broad range of algorithmic techniques reveals that g...
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In recent years, data examples have been at the core of several different approaches to schema-mapping design. In particular, Gottlob and Senellart introduced a framework for schema-mapping discovery from a single dat...
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In recent years, data examples have been at the core of several different approaches to schema-mapping design. In particular, Gottlob and Senellart introduced a framework for schema-mapping discovery from a single data example, in which the derivation of a schema mapping is cast as an optimization problem. Our goal is to refine and study this framework in more depth. Among other results, we design a polynomial-time log(n)-approximation algorithm for computing optimal schema mappings from a given set of data examples (where nis the combined size of the given data examples) for a restricted class of schema mappings;moreover, we show that this approximation ratio cannot be improved. In addition to the complexity-theoretic results, we implemented the aforementioned log(n)-approximation algorithm and carried out an experimental evaluation in a real-world mapping scenario.
Fast constant factor approximation algorithms are devised for an NP- and W[1]hard problem of intersecting a set of n straight line segments with the smallest cardinality set of disks of fixed radii r > 0, where the...
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Given a simple graph G = (V, E) and a constant integer k ≥ 2, the k-path vertex cover problem (PkVC) asks for a minimum subset F ⊆ V of vertices such that the induced subgraph G[V −F] does not contain any path of ord...
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In this work, we study the trade-off between the running time of approximation algorithms and their approximation guarantees. By leveraging a structure of the "hard" instances of the Arora-Rao-Vazirani lemma...
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