Minimizing breaks by maximizing cuts

Minimizing breaks by maximizing cuts

We propose to solve the break minimization problem in sports scheduling by transforming it into a maximum cut problem in an undirected graph and applying a branch-and-cut algorithm. Our approach outperforms previous approaches with constraint programming and integer programming techniques.

Minimizing Breaks by Maximizing

Maximizing Several Cuts Simultaneously

Consider two graphs G1 and G2 on the same vertex set V and suppose that Gi has mi edges. Then there is a bipartition of V into two classes A and B so that for both i = 1, 2 we have eGi(A,B) ≥ mi/2 − √ mi. This answers a question of Bollobás and Scott. We also prove results about partitions into more than two vertex classes.

Breaks, cuts, and patterns

We generalize the concept of a break by considering pairs of arbitrary rounds. We show that a set of home-away 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.

Maximizing Boosted Top Identification by Minimizing N-subjettiness

N -subjettiness is a jet shape designed to identify boosted hadronic objects such as top quarks. Given N subjet axes within a jet, N -subjettiness sums the angular distances of jet constituents to their nearest subjet axis. Here, we generalize and improve on N -subjettiness by minimizing over all possible subjet directions, using a new variant of the k-means clustering algorithm. On boosted top...