DMCA
Break the "right" cycles and get the "best" drawing (2000)
| Venue: | Proc. of the 2nd International Workshop on Algorithm Engineering and Experiments (ALENEX'00 |
| Citations: | 2 - 2 self |
BibTeX
@INPROCEEDINGS{Demetrescu00breakthe,
author = {Camil Demetrescu},
title = {Break the "right" cycles and get the "best" drawing},
booktitle = {Proc. of the 2nd International Workshop on Algorithm Engineering and Experiments (ALENEX'00},
year = {2000},
pages = {171--182}
}
Share
 |
 |
 |
 |
||
OpenURL
Abstract
We consider the two-layer crossing minimization problem (CP): given a two-layered graph and a permutation of the vertices on a layer, find a permutation of the vertices on the other layer so that the number of edge crossings is minimum. Solving CP represents a fundamental step in the construction of aesthetically pleasing layouts of hierarchies and directed graphs. As CP has been proved to be NP-complete, several heuristics for it have been designed, but unfortunately, according to previous experimental results, even algorithms with good theoretical performances appear not to be really effective in practice. The contribution of this paper is twofold. Starting from the penalty minimization technique suggested by Sugiyama, Tagawa, and Toda, we first design a relaxed penalty minimization scheme (in short, RPMS) that yields polynomial time approximation algorithms for CP based on the computation of feedback arc sets. According to these theoretical results, we show an example of application of RPMS and we devise a new approximation algorithm for the two-layer crossing problem, called PM. Then, we perform an experimental analysis of algorithm PM both on randomly generated bipartite graphs and on pathological instances for CP. In particular, we compare the performances of PM, with respect to the number of edge crossings and to the running time, to the performances of three classical algorithms for CP: the barycenter heuristic, an enhanced version of the median algorithm, and a recent attractive greedy strategy. Our experimental results show that algorithm PM stands out as a practical and effective method for minimizing crossings in bipartite drawings. 1. INTRODUCTION Directed graphs are well suitable for representing any kind of structured information. Hence, producing aesthetically pleasing layouts for them finds natural applicability in a wide variety of areas, such as information visualization, software engineering, and graphic user interfaces.
Keyphrases
right quot algorithm pm edge crossing natural applicability recent attractive greedy strategy several heuristic new approximation algorithm graphic user interface pathological instance penalty minimization technique feedback arc set previous experimental result barycenter heuristic structured information bipartite graph running time classical algorithm enhanced version minimization problem two-layer crossing problem good theoretical performance information visualization polynomial time approximation algorithm fundamental step relaxed penalty minimization scheme effective method introduction directed graph two-layered graph bipartite drawing software engineering wide variety theoretical result experimental result median algorithm experimental analysis
