A Computationally Intractable Problem on Simplicial Complexes

Report ID: 
1993-01
Authors: 
Omer Egecioglu and Teofilo Gonzalez
Date: 
1993-01-01 04:00:00

Abstract

We analyze the problem of computing the minimum number er(C) of internalsimplexes that need to be removed from a simplicial 2-complex C so that theremaining complex can be nulled by deleting a sequence of external simplexes.This is equivalent to requiring that the resulting complex be collapsible to a1-complex. By reducing a restricted version of SAT, we show that this problemis NP-complete and therefore computationally intractable. This implies thatthere is no simple formula for er(C) terms of the Betti numbers of thecomplex. The problem remains NP-complete for higher dimensional complexes, butcan be solved in polynomial time for graphs.

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