Vangelis Th. Paschos's Combinatorial Optimization and Theoretical Computer Science: PDF

By Vangelis Th. Paschos

ISBN-10: 1848210213

ISBN-13: 9781848210219

This quantity is devoted to the topic “Combinatorial Optimization – Theoretical desktop technology: Interfaces and views” and has major ambitions: the 1st is to teach that bringing jointly operational learn and theoretical machine technological know-how can yield valuable effects for quite a number purposes, whereas the second one is to illustrate the standard and diversity of study carried out by way of the LAMSADE in those components.

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The number of criteria, is larger than 2. We first give some non-approximability results related to the number of generated solutions for the k-criteria T SP (1, 2). Afterwards, a generalization of 2NN, which has a better complexity than BLS, is proposed. ) time a curve for the k-criteria T SP (1, 2) when k 3. k−1 k+1 -approximate Pareto Let us observe here that the dependence of the time complexity on k! is not surprising since the size of the approximate ε-Pareto curve is not necessarily polynomial on the number of the optimization criteria [PAP 00].

S2n−1 s2n of total distance (3n, 3n) 52 Optimization and Computer Science while tour s1 s3 s2n s4 . . sn+3 sn+1 sn+2 s2 has a total distance of (2n + 1, 2n + 1). In the next section, we deal with a subcase of the bicriteria Max T SP (1, 2) problem. 4. 2, we saw that BM AX LS gives a 1/3-approximate Pareto curve for the bicriteria Max T SP (1, 2) problem. In this section we improve this performance ratio, but only when we restrict the distances vector to edges with distance vectors (1, 2) and (2, 1).

3 allow us to obtain a 1/3-approximate Pareto curve. – The set of solutions returned by BM AX LS is a 1/3-approximate Pareto curve for the bicriteria Max T SP (1, 2) problem. Moreover, this bound is asymptotically sharp. 3. A nearest neighbor heuristic for the bicriteria T SP (1, 2) We now propose a nearest neighbor heuristic which calculates in O(n2 ) a 1/2approximate Pareto curve for the bicriteria M in T SP (1, 2). The idea of this traditional heuristic, applied to a mono-criterion T SP instance, consists of starting from a randomly chosen node and greedily inserting non-visited vertices, which are chosen as those closest to the last inserted vertex [ROS 77].

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Combinatorial Optimization and Theoretical Computer Science: Interfaces and Perspectives by Vangelis Th. Paschos

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