Two-dimensional packing algorithms for layout of disconnected graphs

Two-dimensional packing algorithms for layout of disconnected graphs

We present and contrast several efficient two-dimensional packing algorithms for specified aspect ratio. These near-linear algorithms are based on strip packing, tiling, and alternate-bisection methodologies and can be used in the layout of disconnected objects in graph visualization. The parameters that affect the performance of these algorithms as well as the circumstances under which they pe...

A Comparative Study of Exact Algorithms for the Two Dimensional Strip Packing Problem

In this paper we consider a two dimensional strip packing problem. The problem consists of packing a set of rectangular items in one strip of width W and infinite height. They must be packed without overlapping, parallel to the edge of the strip and we assume that the items are oriented, i.e. they cannot be rotated. To solve this problem, we use three exact methods: a branch and bound method, a...

On two-dimensional Cayley graphs

A subset W of the vertices of a graph G is a resolving set for G when for each pair of distinct vertices u,v in V (G) there exists w in W such that d(u,w)≠d(v,w). The cardinality of a minimum resolving set for G is the metric dimension of G. This concept has applications in many diverse areas including network discovery, robot navigation, image processing, combinatorial search and optimization....

MATHEMATICAL ENGINEERING TECHNICAL REPORTS Practical Algorithms for Two-dimensional Packing

Approximation algorithms for scheduling and two-dimensional packing problems

This dissertation thesis is concerned with two topics of combinatorial optimization: scheduling and geometrical packing problems. Scheduling deals with the assignment of jobs to machines in a ‘good’ way, for suitable notions of good. Two particular problems are studied in depth: on the one hand, we consider the impact of machine failure on online scheduling, i.e. what are the consequences of th...