Minimizing breaks by maximizing cuts

Minimizing Breaks by Maximizing

Most balanced minimum cuts and partially ordered knapsack

We consider the problem of finding most balanced cuts among minimum st-edge cuts and minimum st-vertex cuts, for given vertices s and t, according to different balance criteria. For edge cuts [S, S] we seek to maximize min{|S|, |S|}. For vertex cuts C of G we consider the objectives of (i) maximizing min{|S|, |T |}, where {S, T} is a partition of V (G)\C with s ∈ S, t ∈ T and [S, T ] = ∅, (ii) ...

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.

Local Guarantees in Graph Cuts and Clustering

Correlation Clustering is an elegant model that captures fundamental graph cut problems such as Min s − t Cut, Multiway Cut, and Multicut, extensively studied in combinatorial optimization. Here, we are given a graph with edges labeled + or − and the goal is to produce a clustering that agrees with the labels as much as possible: + edges within clusters and − edges across clusters. The classica...

MATHSM: medial axis transform toward high speed machining of pockets

The pocketing operation is a fundamental procedure in NC machining. Typical pocketing schemes compute uniform successive offsets or parallel cuts of the outline of the pocket, resulting in a toolpath with C discontinuities. These discontinuities render the toolpath quite impractical in the context of high speed machining (HSM). This work addresses and fully resolves the need for a C continuous ...