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DAM
2007
141views more  DAM 2007»
13 years 5 months ago
On the packing chromatic number of Cartesian products, hexagonal lattice, and trees
The packing chromatic number χρ(G) of a graph G is the smallest integer k such that the vertex set of G can be partitioned into packings with pairwise different widths. Several...
Bostjan Bresar, Sandi Klavzar, Douglas F. Rall
COMBINATORICS
2000
95views more  COMBINATORICS 2000»
13 years 5 months ago
Improving Dense Packings of Equal Disks in a Square
We describe a new numerical procedure for generating dense packings of disks and spheres inside various geometric shapes. We believe that in some of the smaller cases, these packi...
David W. Boll, Jerry Donovan, Ronald L. Graham, Bo...
CORR
2008
Springer
103views Education» more  CORR 2008»
13 years 5 months ago
Packing multiway cuts in capacitated graphs
We consider the following "multiway cut packing" problem in undirected graphs: we are given a graph G = (V, E) and k commodities, each corresponding to a set of terminal...
Siddharth Barman, Shuchi Chawla
IPCO
2008
129views Optimization» more  IPCO 2008»
13 years 6 months ago
A Polynomial Time Approximation Scheme for the Square Packing Problem
Given a set Q of squares with positive pro ts, the square packing problem is to select and pack a subset of squares of maximum pro t into a rectangular bin R. We present a polynomi...
Klaus Jansen, Roberto Solis-Oba
CP
2008
Springer
13 years 6 months ago
Search Strategies for Rectangle Packing
Rectangle (square) packing problems involve packing all squares with sizes 1 × 1 to n × n into the minimum area enclosing rectangle (respectively, square). Rectangle packing is a...
Helmut Simonis, Barry O'Sullivan