
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
41st Annual Symposium on Foundations of Computer Science
Nested graph dissection and approximation algorithms
Redondo Beach, California
November 12November 14
ISBN: 0769508502
ASCII Text  x  
S. Guha, "Nested graph dissection and approximation algorithms," 2013 IEEE 54th Annual Symposium on Foundations of Computer Science, pp. 126, 41st Annual Symposium on Foundations of Computer Science, 2000.  
BibTex  x  
@article{ 10.1109/SFCS.2000.892072, author = {S. Guha}, title = {Nested graph dissection and approximation algorithms}, journal ={2013 IEEE 54th Annual Symposium on Foundations of Computer Science}, volume = {0}, year = {2000}, issn = {02725428}, pages = {126}, doi = {http://doi.ieeecomputersociety.org/10.1109/SFCS.2000.892072}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  CONF JO  2013 IEEE 54th Annual Symposium on Foundations of Computer Science TI  Nested graph dissection and approximation algorithms SN  02725428 SP EP A1  S. Guha, PY  2000 KW  computational geometry; approximation theory; graph theory; polynomials; nested graph dissection; approximation algorithms; nested dissection paradigm; upper bound; chordal completion size; polynomial term; vertex ranking; planar embedding VL  0 JA  2013 IEEE 54th Annual Symposium on Foundations of Computer Science ER   
This paper considers approximation algorithms for graph completion problems using the nested dissection paradigm. Given a superadditive function of interest (the smallest planar or chordal extension for example) and a test that relates it to an upper bound of the smallest separator, we provide a framework how to dissect the graph recursively such that no subgraph has more than half the value of its parent, (or is indistinguishable via separator tests) in polynomial time. Interestingly we cannot bound such a function till we have constructed the entire nested dissection. We achieve a partition of the graph with respect to a constant number of such unknown estimator functions simultaneously. Using the framework the paper presents improvements in approximating the chordal completion size (by a factor of log n), operation count (by a factor of log/sup 2/ n and the polynomial term depending on degree) and elimination height. We show that there exists a nested dissection ordering that simultaneously minimizes the elimination height, chordal completion, operation count to within O(log n) factors of the best possible (which may be obtained by three independent orderings) improving the previous existence theorem by factors of log n and d/sup 1/3/ log/sup 3/ n for the latter two. We also show that graphs with small crossing number or fillin have better approximations of the elimination height, completion and operation count. As a consequence we can approximate the pathwidth, cutwidth, vertex ranking problems better for such graphs. The paper also improves, in some cases, the approximation results of minimum drawing size (number of vertices plus the crossing number) of a planar embedding of a graph, and its layout area on a grid.
Index Terms:
computational geometry; approximation theory; graph theory; polynomials; nested graph dissection; approximation algorithms; nested dissection paradigm; upper bound; chordal completion size; polynomial term; vertex ranking; planar embedding
Citation:
S. Guha, "Nested graph dissection and approximation algorithms," focs, pp.126, 41st Annual Symposium on Foundations of Computer Science, 2000
Usage of this product signifies your acceptance of the Terms of Use.