Arie Tamir

On the complexity of locating linear facilities in the plane

We consider the computational complexity of linear facility location problems in the plane, i.e., given n demand points, one wishes to find r lines so as to minimize a certain objective-function reflecting the need of the points to be close to the lines. It is shown that it is NP-hard to find r lines so as to minimize any isotone function of the distances between given points and their respective nearest lines. The proofs establish NP-hardness in the strong sense. The results also apply to the situation where the demand is represented by r lines and the facilities by n single points.

Approximation algorithms for maximum dispersion

We describe approximation algorithms with bounded performance guarantees for the following problem: A graph is given with edge weights satisfying the triangle inequality, together with two numbers k and p. Find k disjoint subsets of p vertices each, so that the total weight of edges within subsets is maximized

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Many known algorithms are based on selection in a set whose cardinality is superlinear in terms of the input length. It is desirable in these cases to have selection algorithms that run in sublinear time in terms of the cardinality of the set. This paper presents a successful development in this direction. The methods developed here are applied to improve the previously known upper bounds for the time complexity of various location problems.

O(n\log ^2 n)

In this note we apply recent results in dynamic programming to improve the complexity bounds of several median and coverage location models on the real line.

Algorithm for the kth Longest Path in a Tree with Applications to Location Problems

This paper discusses new complexity results for several models dealing with the location of obnoxious or undesirable facilities on graphs. The focus is mainly on the continuous p-Maximin and p-Maxisum dispersion models, where the facilities can be established at the nodes or in the interiors of the edges. For the general (nonhomogeneous) case it is shown that both models are strongly NP-hard even when the underlying graph consists of a single edge.For the homogeneous p-Maximin model it is proven that even the problem of finding a

Improved complexity bounds for location problems on the real line

\frac{2}{3}

Obnoxious facility location on graphs

-approximation solution is NP-hard, and a polynomial heuristic which provides a

NEW RESULTS ON THE COMPLEXITY OF p-CENTER PROBLEMS*

\frac{1}{2}

Minimizing the sum of the k largest functions in linear time

-approximation to the model is presented. Tree graphs are considered, and new algorithms with lower complexity bounds for several versions of the model are presented.For the p-Maxisum problem we show that the homogeneous case is NP-hard on general graphs. Turning to the homogeneous case on trees, a certain concavity property is identified and then utilized to improve upon the...

On the minimum diameter spanning tree problem

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