Crossing Number for Graphs with Bounded Pathwidth
نویسندگان
چکیده
منابع مشابه
Crossing Number for Graphs with Bounded~Pathwidth
The crossing number is the smallest number of pairwise edge-crossings when drawing a graph into the plane. There are only very few graph classes for which the exact crossing number is known or for which there at least exist constant approximation ratios. Furthermore, up to now, general crossing number computations have never been successfully tackled using bounded width of graph decompositions,...
متن کاملLight Spanners in Bounded Pathwidth Graphs
In approximation algorithm design, light spanners has applications in graph-metric problems such as metric TSP (the traveling salesman problem) [8] and others [3]. We have developed an efficient algorithm in [9] for light spanners in bounded pathwidth graphs, based on an intermediate data structure called monotone tree. In this paper, we extended the results to include bounded catwidth graphs.
متن کاملFinding Light Spanners in Bounded Pathwidth Graphs
Given an edge-weighted graph G and > 0, a (1+ )-spanner is a spanning subgraph G′ whose shortest path distances approximate those of G within a factor of 1+ . For G from certain graph families (such as bounded genus graphs and apex graphs), we know that light spanners exist. That is, we can compute a (1+ )-spanner G′ with total edge weight at most a constant times the weight of a minimum spanni...
متن کاملRandomly coloring graphs of logarithmically bounded pathwidth
We consider the problem of sampling a proper k-coloring of a graph of maximal degree ∆ uniformly at random. We describe a new Markov chain for sampling colorings, and show that it mixes rapidly on graphs of logarithmically bounded pathwidth if k ≥ (1+ )∆, for any > 0, using a new hybrid paths argument. ∗California Institute of Technology, Pasadena, CA, 91125, USA. E-mail: [email protected].
متن کاملMETA-HEURISTIC ALGORITHMS FOR MINIMIZING THE NUMBER OF CROSSING OF COMPLETE GRAPHS AND COMPLETE BIPARTITE GRAPHS
The minimum crossing number problem is among the oldest and most fundamental problems arising in the area of automatic graph drawing. In this paper, eight population-based meta-heuristic algorithms are utilized to tackle the minimum crossing number problem for two special types of graphs, namely complete graphs and complete bipartite graphs. A 2-page book drawing representation is employed for ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Algorithmica
سال: 2020
ISSN: 0178-4617,1432-0541
DOI: 10.1007/s00453-019-00653-x