Graduate Thesis Or Dissertation

 

Computing Bounded Chains and Surfaces in a Simplicial Complex with Bounded-treewidth 1-skeleton Public Deposited

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https://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/bv73c697f

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  • We consider three problems on simplicial complexes: the Optimal Bounded Chain Problem, the Optimal Homologous Chain Problem, and 2-Dim-Bounded-Surface. The Optimal Bounded Chain Problem asks to find the minimum weight d-chain in a simplicial complex K bounded by a given (d−1)-chain, if such a d-chain exists. The Optimal Homologous Chain problem asks to find the minimum weight (d−1)-chain in K homologous to a given (d−1)-chain. 2-Dim-Bounded-Surface asks whether or not there is a subcomplex of K homeomorphic to a given compact, connected surface bounded by a given subcomplex. All three problems are NP-hard, and the first two problems are hard to approximate within any constant factor assuming the Unique Games Conjecture. We prove that all three problems are fixed-parameter tractable with respect to the treewidth of the 1-skeleton of K.
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