The carryover effect does not influence football results

In a round robin tournament, it is often believed that each team has an effect on its opponent, which carries over to the next game of that opponent. Indeed, if team A plays against team B, and subsequently against team C, A’s performance against C may have been affected by B, and we say that team C receives a carryover effect from B. For instance, if team B is a very strong team, then team A could be exhausted and discouraged after this game, which could benefit its next opponent, team C. Clearly, any schedule will lead to carryover effects. In practice, the perceived influence of carryover effects has been used as an argument when producing a schedule. In this work, we develop an approach to measure whether carryover effects have an influence on the outcome of football matches. The authors apply this method on the highest division in Belgium, using data from over 30 seasons, amounting over 10,000 matches. In our data set, we find no evidence to support the claim that carryover effects affect the results, which has major implications for the sporting community with respect to generating fixtures.status: publishe

The temporal explorer who returns to the base.

In this paper we study the problem of exploring a temporal graph (i.e. a graph that changes over time), in the fundamental case where the underlying static graph is a star on n vertices. The aim of the exploration problem in a temporal star is to find a temporal walk which starts at the center of the star, visits all leaves, and eventually returns back to the center. We present here a systematic study of the computational complexity of this problem, depending on the number k of time-labels that every edge is allowed to have; that is, on the number k of time points where each edge can be present in the graph. To do so, we distinguish between the decision version STAREXP(k) , asking whether a complete exploration of the instance exists, and the maximization version MAXSTAREXP(k) of the problem, asking for an exploration schedule of the greatest possible number of edges in the star. We fully characterize MAXSTAREXP(k) and show a dichotomy in terms of its complexity: on one hand, we show that for both k=2 and k=3 , it can be efficiently solved in O(nlogn) time; on the other hand, we show that it is APX-complete, for every k≥4 (does not admit a PTAS, unless P = NP, but admits a polynomial-time 1.582-approximation algorithm). We also partially characterize STAREXP(k) in terms of complexity: we show that it can be efficiently solved in O(nlogn) time for k∈{2,3} (as a corollary of the solution to MAXSTAREXP(k) , for k∈{2,3} ), but is NP-complete, for every k≥6

Online interval scheduling on two related machines:the power of lookahead

\u3cp\u3eWe consider an online interval scheduling problem on two related machines. If one machine is at least as twice as fast as the other machine, we say the machines are distinct; otherwise the machines are said to be similar. Each job j∈ J is characterized by a length p\u3csub\u3ej\u3c/sub\u3e, and an arrival time t\u3csub\u3ej\u3c/sub\u3e; the question is to determine whether there exists a feasible schedule such that each job starts processing at its arrival time. For the case of unit-length jobs, we prove that when the two machines are distinct, there is an amount of lookahead allowing an online algorithm to solve the problem. When the two machines are similar, we show that no finite amount of lookahead is sufficient to solve the problem in an online fashion. We extend these results to jobs having arbitrary lengths, and consider an extension focused on minimizing total waiting time.\u3c/p\u3

Valid inequalities for a time-indexed formulation

We present a general time-indexed formulation that contains scheduling problems with unrelated parallel machines. We derive a class of basic valid inequalities for this formulation, and we show that a subset of these inequalities are facet-defining. We characterize all facet-defining inequalities with right-hand side 1. Further, we show how to efficiently separate these inequalitie

An LP-based algorithm for the data association problem in multitarget tracking

\u3cp\u3eIn this paper we present a linear programming (LP) based approach for solving the data association problem (DAP) in multiple target tracking. It is well-known that the DAP can be formulated as an integer program. We present a compact formulation of the DAP. To solve practical instances of the DAP we propose an algorithm that uses an iterated K-scan sliding window technique. In each iteration we solve the linear programming relaxation of an integer program and next apply a greedy rounding procedure. Computational experiments indicate that the quality of the solutions found is quite satisfactory.\u3c/p\u3