An Algorithm for Packing Squares

An Algorithm for Packing Connectors

Given an undirected graph G = (V; E) and a partition fS; Tg of V , an S{T connector is a set of edges F E such that every component of the subgraph (V; F) intersects both S and T. If either S or T is a singleton, then an S{T connector is a spanning tree of G. On the other hand, if G is bipartite with colour classes S and T, then an S{T connector is an edge cover of G (a set of edges covering al...

An Incremental DC Algorithm for the Minimum Sum-of-Squares Clustering

Here, an algorithm is presented for solving the minimum sum-of-squares clustering problems using their difference of convex representations. The proposed algorithm is based on an incremental approach and applies the well known DC algorithm at each iteration. The proposed algorithm is tested and compared with other clustering algorithms using large real world data sets.

On Packing Squares with Equal Squares

The following problem arises in connection with certain multidimensional stock cutting problems : How many nonoverlapping open unit squares may be packed into a large square of side a? Of course, if a is a positive integer, it is trivial to see that a2 unit squares can be successfully packed . However, if a is not an integer, the problem becomes much more complicated . Intuitively, one feels th...

Translative Packing of Unit Squares into Squares

An Approximation Algorithm for Maximum Triangle Packing

We present a randomized ( 89 169 − )-approximation algorithm for the weighted maximum triangle packing problem, for any given > 0. This is the first algorithm for this problem whose performance guarantee is better than 1 2 . The algorithm also improves the best-known approximation bound for the maximum 2-edge path packing problem. © 2005 Elsevier B.V. All rights reserved.