Breaks, cuts, and patterns

Wegeneralize the concept of a break by considering pairs of arbitrary rounds.Weshow that a set of homeaway patterns minimizing the number of generalized breaks cannot be found in polynomial time, unless P = NP. When all teams have the same break set, the decision version becomes easy; optimizing remains NP-hard.status: publishe

Soccer schedules in Europe: an overview

In this paper, we give an overview of the competition formats and the schedules used in 25 European soccer competitions for the season 2008-2009. We discuss how competitions decide the league champion, qualification for European tournaments, and relegation. Following Griggs and Rosa (Bull. ICA 18:65-68, 1996), we examine the popularity of the so-called canonical schedule. We investigate the presence of a number of properties related to successive home or successive away matches (breaks) and of symmetry between the various parts of the competition. We introduce the concept of ranking-balancedness, which is particularly useful to decide whether a fair ranking can be made. We also determine how the schedules manage the carry-over effect. We conclude by observing that there is quite some diversity in European soccer schedules, and that current schedules leave room for further optimizing

Facets of the axial three-index assignment polytope

We revisit the facial structure of the axial 3-index assignment polytope. After reviewing known classes of facet-defining inequalities, we present a new class of valid inequalities, and show that they are facets of this polytope. This answers a question posed by Qi and Sun~\cite{QiSun00}. Moreover, we show that we can separate these inequalities in polynomial time

The lockmaster's problem.

Inland waterways form a natural network that is an existing, congestion free infrastructure with capacity for more traffic.Transportation of goods by ship is widely promoted as it is a reliable, efficient and environmental friendly way of transport. A bottleneck for transportation over water are the locks that manage the water level. The lockmaster's problem concerns the optimal strategy for operating such a lock. In the lockmaster's problem we are given a lock, a set of ships coming from downstream that want to go upstream, and another set of ships coming from upstream that want to go downstream. We are given the arrival times of the ships and a constant lockage time; the goal is to minimize total waiting time of the ships. In this paper a dynamic programming algorithm (DP) is proposed that solves the lockmaster's problem in polynomial time. We extend this DP to different generalizations that consider weights, water usage, capacity, and (a fixed number of) multiple chambers. Finally, we prove that the problem becomes strongly NP-hard when the number of chambers is part of the input.Lock scheduling; Batch scheduling; Dynamic programming; Complexity;

Approximating the multi-level bottleneck assignment problem.

We consider the multi-level bottleneck assignment problem (MBA). This problem is described in the recent book 'Assignment Problems' by Burkard et al. (2009) on pages 188-189. One of the applications described there concerns bus driver scheduling.We view the problem as a special case of a bottleneck m-dimensional multi-index assignment problem. We give approximation algorithms and inapproximability results, depending upon the completeness of the underlying graph. Keywords: bottleneck problem; multidimensional assignment; approximation; computational complexity; efficient algorithm.Bottleneck problem; Multidimensional assignment; Approximation; Computational complexity; Efficient algorithm;

Facets of the axial three-index assignment polytope

We revisit the facial structure of the axial 3-index assignment polytope. After reviewing known classes of facet-defining inequalities, we present a new class of valid inequalities, and show that they define facets of this polytope. This answers a question posed by Qi and Sun (2000). Moreover, we show that we can separate these inequalities in polynomial time. Finally, we assess the computational relevance of the new inequalities by performing (limited) computational experiments