Annette M. C. Ficker

Round-Robin Tournaments Generated by the Circle Method Have Maximum Carry-Over

The Circle Method is widely used in the field of sport scheduling to generate schedules for round-robini¾źtournaments. The so-called carry-over effect value is a number that can be associated to each round-robin schedule; it represents a degree of balance of a schedule. Here, we prove that, for an even number of teams, the Circle Method generates a schedule with maximum carry-over effect value, answering an open question.

Balanced optimization with vector costs

We consider so-called balanced optimization problems with vector costs. We propose a framework containing such problems; this framework allows us to investigate the complexity and approximability of these problems in a general setting. More concrete, each problem in the framework admits a 2-approximation, and for many problems within the framework this result is best-possible, in the sense that having a polynomial-time algorithm with a performance ratio better than 2 would imply P=NP. Special attention is paid to the balanced assignment problem with vector costs: we show that the problem remains NP-hard even in case of sum costs.