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Simplicial complexes and the Optimal...

Smith, Gavin W.

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Simplicial complexes and the Optimal Homologous Chain Problem.

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Simplicial complexes and the Optimal Homologous Chain Problem./
作者:	Smith, Gavin W.
面頁冊數:	78 p.
附註:	Source: Dissertation Abstracts International, Volume: 74-11(E), Section: A.
Contained By:	Dissertation Abstracts International74-11A(E).
標題:	Business Administration, Marketing. -
電子資源:	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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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.
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