NDLI: Subexponential parameterized algorithms on bounded-genus graphs and $\textit{H}-minor-free$ graphs

Content Provider	ACM Digital Library
Author	Demaine, Erik D. Fomin, Fedor V. Hajiaghayi, Mohammadtaghi Thilikos, Dimitrios M.
Copyright Year	2005
Abstract	We introduce a new framework for designing fixed-parameter algorithms with subexponential running $time---2^{O(&kradic;)}$ $n^{O(1)}.$ Our results apply to a broad family of graph problems, called bidimensional problems, which includes many domination and problems such as vertex cover, feedback vertex set, minimum maximal matching, dominating set, edge dominating set, disk dimension, and many others restricted to bounded-genus graphs (phrased as bipartite-graph problem). Furthermore, it is fairly straightforward to prove that a problem is bidimensional. In particular, our framework includes, as special cases, all previously known problems to have such subexponential algorithms. Previously, these algorithms applied to planar graphs, single-crossing-minor-free graphs, and/or map graphs; we extend these results to apply to bounded-genus graphs as well. In a parallel development of combinatorial results, we establish an upper bound on the treewidth (or branchwidth) of a bounded-genus graph that excludes some planar graph $\textit{H}$ as a minor. This bound depends linearly on the size $\textit{¦V(H)¦}$ of the excluded graph $\textit{H}$ and the genus $\textit{g(G)}$ of the graph $\textit{G},$ and applies and extends the graph-minors work of Robertson and Seymour.Building on these results, we develop subexponential fixed-parameter algorithms for dominating set, vertex cover, and set cover in any class of graphs excluding a fixed graph $\textit{H}$ as a minor. In particular, this general category of graphs includes planar graphs, bounded-genus graphs, single-crossing-minor-free graphs, and any class of graphs that is closed under taking minors. Specifically, the running time is $2^{O(&kracic;)}$ $n^{h},$ where $\textit{h}$ is a constant depending only on $\textit{H},$ which is polynomial for $\textit{k}$ = $O(log^{2}$ $\textit{n}).$ We introduce a general approach for developing algorithms on $\textit{H}-minor-free$ graphs, based on structural results about $\textit{H}-minor-free$ graphs at the heart of Robertson and Seymour's graph-minors work. We believe this approach opens the way to further development on problems in $\textit{H}-minor-free$ graphs.
Starting Page	866
Ending Page	893
Page Count	28
File Format	PDF
ISSN	00045411
e-ISSN	1557735X
DOI	10.1145/1101821.1101823
Journal	Journal of the ACM (JACM)
Volume Number	52
Issue Number	6
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2005-11-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	(k,r)-center Domination Fixed-parameter algorithms Map graph Planar graph
Content Type	Text
Resource Type	Article
Subject	Hardware and Architecture Information Systems Control and Systems Engineering Artificial Intelligence Software

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Fixed-parameter algorithms for $(\textit{k},$ $\textit{r})-center$ in planar graphs and map graphs

Subexponential Parameterized Algorithms on Graphs of Bounded Genus and H-Minor-Free Graphs (2003)

Subexponential parameterized algorithms on graphs of bounded genus and h-minor-free graphs (2004).

Subexponential parameterized algorithms on graphs of bounded genus and H-minor-free graphs (2003)

Subexponential parameterized algorithms on graphs of bounded genus and H-minor-free graphs (2004)

Subexponential Parameterized Algorithms on Bounded-Genus Graphs and H-Minor-Free Graphs (2005)

Subexponential parameterized algorithms on graphs of bounded-genus and H-minor-free graphs

Fixed-Parameter Algorithms for the (k, r)-Center in Planar Graphs and Map Graphs (2003)

Fixed-Parameter Algorithms for the (k, r)-Center in Planar Graphs and Map Graphs

Subexponential parameterized algorithms on bounded-genus graphs and $\textit{H}-minor-free$ graphs

Similar Documents

Fixed-parameter algorithms for $(\textit{k},$ $\textit{r})-center$ in planar graphs and map graphs

Subexponential Parameterized Algorithms on Graphs of Bounded Genus and H-Minor-Free Graphs (2003)

Subexponential parameterized algorithms on graphs of bounded genus and h-minor-free graphs (2004).

Subexponential parameterized algorithms on graphs of bounded genus and H-minor-free graphs (2003)

Subexponential parameterized algorithms on graphs of bounded genus and H-minor-free graphs (2004)

Subexponential Parameterized Algorithms on Bounded-Genus Graphs and H-Minor-Free Graphs (2005)

Subexponential parameterized algorithms on graphs of bounded-genus and H-minor-free graphs

Fixed-Parameter Algorithms for the (k, r)-Center in Planar Graphs and Map Graphs (2003)

Fixed-Parameter Algorithms for the (k, r)-Center in Planar Graphs and Map Graphs

Subexponential parameterized algorithms on bounded-genus graphs and $\textit{H}-minor-free$ graphs