In this paper, we prove that both problems for calculating the Banzhaf power index and the Shapley–Shubik power index for weighted majority games are NP-complete.
Unit disk graphs are the intersection graphs of equal sized circles in the plane. In this paper, we consider the maximum independent set problems on unit disk graphs. When the given unit disk graph is dened on a slab whose width is k, we propose an algorithm for nding a maximum independent set in O(n 4d2k= p 3e) time where n denotes the number of vertices.… (More)
In sports timetabling, creating an appropriate timetable for a round-robin tournament with home–away assignment is a significant problem. To solve this problem, we need to construct home–away assignment that can be completed into a timetable; such assignment is called a feasible pattern set. Although finding feasible pattern sets is at the heart of many… (More)
Consider two orthogonal closed chains on a cylinder. The chains are monotone with respect to the angle Θ. We wish to rigidly move one chain so that the total area between the two chains is minimized. This is a geometric measure of similarity between two repeating melodies proposed by´O Maidín. We present an O(n) time algorithm to compute this measure if Θ… (More)
Consider two orthogonal closed chains on a cylinder. These chains are monotone with respect to the tangential Θ direction. We wish to rigidly move one chain so that the total area between the two is minimized. This minimization is a geometric measure of similarity between two melodies proposed by´O Maidín. The Θ direction represents time and the axial… (More)
We propose a polynomial-time algorithm to find an equitable home–away assignment for a given timetable of a round-robin tournament. Our results give an answer to a problem raised by Elf et al. (Oper. Res. Lett. 31 (2003) 343), which concerns the computational complexity of the break minimization problem in sports timetabling.
This paper considers the break minimization problem in sports timetabling. The problem is to find, under a given timetable of a round-robin tournament, a home-away assignment that minimizes the number of breaks, i.e., the number of occurrences of consecutive matches held either both at away or both at home for a team. We formulate the break minimization… (More)