Fast and space-efficient algorithms for deciding shellability of simplicial complexes of large size using h-assignments

Although it is important to decide whether a simplicial complex is shellable or not, no efficient algorithm is known for the problem. We introduce an innovative software SHIDE (SHellability decIDEr) which decides shellability of large-size simplicial complexes. SHIDE traverses the facet-ridge incidence graph of a simplicial complex to find a shelling in a depth-first search fashion which is space-efficient. SHIDE also uses a hashing technique that efficiently checks whether a subproblem has already been solved or not to avoid redundant computation during the traversal. Experimental results show that shellability of almost all simplicial complexes with about 40 facets are decided regardless the dimension within 3 hours using a conventional workstation.