Relaxed voting and competitive location under monotonous gain functions on trees

Authors:
J. Spoerhase;H. -C. Wirth
Affiliations:
Lehrstuhl für Informatik I, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany;Lehrstuhl für Informatik I, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany
Venue:
Discrete Applied Mathematics
Year:
2010

Citing 2
Cited 1

Optimally computing all solutions of Stackelberg with parametric prices and of general monotonous gain functions on a tree

Journal of Discrete Algorithms
Time bounds for selection

Journal of Computer and System Sciences

Optimally computing all solutions of Stackelberg with parametric prices and of general monotonous gain functions on a tree

Journal of Discrete Algorithms

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Abstract

We examine competitive location problems where two competitors serve a good to users located in a network. Users decide for one of the competitors based on the distance induced by an underlying tree graph. The competitors place their server sequentially into the network. The goal of each competitor is to maximize his benefit which depends on the total user demand served. Typical competitive location problems include the (1,X"1)-medianoid, the (1,1)-centroid, and the Stackelberg location problem. An additional relaxation parameter introduces a robustness of the model against small changes in distance. We introduce monotonous gain functions as a general framework to describe the above competitive location problems as well as several problems from the area of voting location such as Simpson, Condorcet, security, and plurality. In this paper we provide a linear running time algorithm for determining an absolute solution in a tree where competitors are allowed to place on nodes or on inner points. Furthermore we discuss the application of our approach to the discrete case.