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Simplicial complexes and the Optimal...

Smith, Gavin W.

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Simplicial complexes and the Optimal Homologous Chain Problem.

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Simplicial complexes and the Optimal Homologous Chain Problem./
Author:	Smith, Gavin W.
Description:	78 p.
Notes:	Source: Dissertation Abstracts International, Volume: 74-11(E), Section: A.
Contained By:	Dissertation Abstracts International74-11A(E).
Subject:	Business Administration, Marketing. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3587174
ISBN:	9781303241987

Simplicial complexes and the Optimal Homologous Chain Problem.
Smith, Gavin W.

Simplicial complexes and the Optimal Homologous Chain Problem. - 78 p.

Source: Dissertation Abstracts International, Volume: 74-11(E), Section: A.

Thesis (Ph.D.)--Washington State University, 2013.

This dissertation examines topological properties of a finite simplicial complex K that ensure any Optimal Homologous Chain Problem (OHCP) with an arbitrary p-dimensional chain as input ( p ∈ N ) can be solved in polynomial time. One such property already known is when the boundary matrix [∂p+1] of K is totally unimodular [6]. This dissertation defines a weaker but related condition for K called NTU-neutralized, and shows this also ensures polynomial time for any OHCP with an arbitrary p-chain input. This is done by defining OHCP over the reals or rationals instead of integers, and formulating the OHCP as an LP. Several properties of basic solutions and vertices of an OHCP LP are also revealed.

ISBN: 9781303241987Subjects--Topical Terms:

1017573
Business Administration, Marketing.

Simplicial complexes and the Optimal Homologous Chain Problem.
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020 $a 9781303241987
035 $a (MiAaPQ)AAI3587174
035 $a AAI3587174
040 $a MiAaPQ $c MiAaPQ
100 1 $a Smith, Gavin W. $3 2100479
245 1 0 $a Simplicial complexes and the Optimal Homologous Chain Problem.
300 $a 78 p.
500 $a Source: Dissertation Abstracts International, Volume: 74-11(E), Section: A.
500 $a Adviser: Bala Krishnamoorthy.
502 $a Thesis (Ph.D.)--Washington State University, 2013.
520 $a This dissertation examines topological properties of a finite simplicial complex K that ensure any Optimal Homologous Chain Problem (OHCP) with an arbitrary p-dimensional chain as input ( p ∈ N ) can be solved in polynomial time. One such property already known is when the boundary matrix [∂p+1] of K is totally unimodular [6]. This dissertation defines a weaker but related condition for K called NTU-neutralized, and shows this also ensures polynomial time for any OHCP with an arbitrary p-chain input. This is done by defining OHCP over the reals or rationals instead of integers, and formulating the OHCP as an LP. Several properties of basic solutions and vertices of an OHCP LP are also revealed.
520 $a This dissertation also studies edge contractions on a finite simplicial complex K, a common operation to simplify complexes. It defines the p-link condition for an edge ab ∈ K. We show that if ab satisfies the p-link condition, and [∂p+1] of K is totally unimodular, then [∂p +1] of the remaining complex after contracting ab is also totally unimodular.
590 $a School code: 0251.
650 4 $a Business Administration, Marketing. $3 1017573
650 4 $a Applied Mathematics. $3 1669109
690 $a 0338
690 $a 0364
710 2 $a Washington State University. $b Mathematics. $3 2100480
773 0 $t Dissertation Abstracts International $g 74-11A(E).
790 $a 0251
791 $a Ph.D.
792 $a 2013
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=3587174