Memorial University DAI: Algorithmic complexity and extremality characterizations for edge searching and its variations

advanced search

Digital Archives Initiative
Memorial University - Electronic Theses and Dissertations 4

menu off

add document to favorites : add page to favorites : reference url

back to results : previous : next

Search this object:

0 hit(s) :: previous hit : next hit

View:

previous page : next page

Document Description

Title	Algorithmic complexity and extremality characterizations for edge searching and its variations
Author	Yasar, Oznur, 1978-
Description	Thesis (Ph.D.)--Memorial University of Newfoundland, 2008. Mathematics and Statistics
Date	2008
Pagination	viii, 101 leaves : ill. (some col.)
Subject	Combinatorial group theory; Graph algorithms;
Degree	Ph.D.
Degree Grantor	Memorial University of Newfoundland. Dept. of Mathematics and Statistics
Discipline	Mathematics and Statistics
Language	Eng
Notes	Includes bibliographical references (leaves 94-99)
Abstract	Edge searching is a combinatorial game played on graphs. The aim is to construct a search strategy to catch an intruder hidden in the graph independent of his actions. If the intruder has a diffused form then searching corresponds to cleaning the graph. A related problem consists of minimizing the number of searchers used in this search. Various versions of edge searching have been introduced in the past depending on how searchers and the intruder can move. In this dissertation we define Weighted Search and Fast Search as two new variants and answer some complexity and extremality problems. -- Weighted Search corresponds to cleaning a contaminated graph where edges may have different capacities. The main result we have is that Weighted Search is an NP-complete problem. We also give comparison results such as bounds on the weighted search number in terms of related graph parameters including pathwidth. We characterize those graphs which two searchers can clean. -- Fast Search is an internal monotone search where no edge is traversed more than once in a non-weighted graph. We present a linear time algorithm to compute a fast search strategy for a given tree. We investigate the fast search strategies for bipartite graphs. -- The construction of k-searchable graphs, those graphs which k searchers can clean, has been of major interest. Graphs that are 1, 2 or 3-searchable have been completely characterized previously, whereas characterizing 4-searchable graphs was left as an open problem. We solve this problem partially and give insights for future work.
Type	Text
Resource Type	Electronic thesis or dissertation
Format	Image/jpeg; Application/pdf
Source	Paper copy kept in the Centre for Newfoundland Studies, Memorial University Libraries
Local Identifier	a2707752
Rights	The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission.
Collection	Electronic Theses and Dissertations
Scanning Status	Completed
PDF File	(9.85 MB) -- http://collections.mun.ca/PDFs/theses/Yasar_Oznur.pdf
CONTENTdm file name	27162.cpd