The number partitioning problem is to divide a given set of n positive integers into k subsets, so that the sum of the numbers in each subset are as nearly equal as possible. While effective algorithms for two-way partitioning exist, multi-way partitioning is much more challenging. We introduce an improved algorithm for optimal multi-way partitioning, by combining several existing algorithms wi...

I INTRODUCTION A basic attribute of the human visual system is its ability to group elements of a perceived scene or visual field into meaningful or coherent clusters; in addition to clustering or partitioning, the visual system generally imparts structure and often a semantic interpretation to the data. In spite of the apparent existence proof provided by human vision, the general problem of s...

Given a finite ground set, a set of subsets, and costs on the subsets, the set partitioning problem is to find a minimum cost partition of the ground set. Many combinatorial optimization problems can be formulated as set partitioning problems. We present an approximation algorithm that produces high-quality solutions in an acceptable amount of computation time. The algorithm is iterative and co...

We introduce a new class of space-time codes called super-orthogonal space-time trellis codes. These codes combine set partitioning and a super set of orthogonal space–time block codes in a systematic way to provide full diversity and improved coding gain over earlier space–time trellis code constructions. We also study the optimality of our set partitioning and provide coding gain analysis. Co...

Given a nite ground set a set of subsets and costs on the subsets the set partitioning problem is to nd a minimum cost partition of the ground set Many combinatorial optimization problems can be formulated as set partitioning problems We present an approximation algorithm that produces high quality solutions in an acceptable amount of computation time The algorithm is iterative and combines pro...

This paper describes an algorithm for partitioning a graph that is in the form of a tree. The algorithm has a growth in computation time and storage requirements that is directly proportional to the number of nodes in the tree. Several applications of the algorithm are briefly described. In particular it is shown that the tree partitioning problem frequently arises in the allocation of computer...