Min-k-cut is the problem of partitioning vertices of a given graph or hypergraph into k subsets such that the total weight of edges or hyperedges crossing different subsets is minimized. For the capacitated min-k-cut problem, each edge has a nonnegative weight, and each subset has a possibly different capacity that imposes an upper bound on its size. The objective is to find a partition that mi...

In practice, cutting large number of pieces with different shapes often requires a well plan of assigning number of shapes on the cut template. The working arrangement of the cut-template is treated as Cut order plan (COP). The aim is to optimize cutting templates of fabric cutting function in apparel manufacturing firms when the cut order requirement is known. This solving of cut order plan pr...

Let A be a set of n arcs on the unit circle. We present a new simple (n logn)-time algorithm for computing a minimum cut set for A (and a maximum independent subset of A). Our solution is based on a dynamic maintenance scheme for a set S of n intervals on the line, that enables us to update the current minimum cut set for S, following an insertion or a deletion of an interval, in time O(c logn)...

One of the steps involved in the computer-aided design for FPGA (FieldProgrammable Gate Array) circuits is placement. In this step, the logic functions are assigned to specific cells of the circuit. In conventional hierarchical min-cut based placement algorithms, the layout region is bi-partitioned using slicing lines in a top-down manner. In these placement algorithms, the cut-line is always c...