Shellings of simplicial complexes have long been a useful tool in topological and algebraic combinatorics. complex expose large amount information helpful way, but are not easy to construct, often requiring deep about the structure complex. It is natural ask whether shellings may be efficiently found computationally. In recent paper, Goaoc, Pat\'ak, Pat\'akov\'a, Tancer Wagner gave negative ans...

In this paper, we study linear CNF formulas generalizing linear hypergraphs un-der combinatorial and complexity theoretical aspects w.r.t. SAT. We establish NP-completeness of SAT for the unrestricted linear formula class, and we show the equiv-alence of NP-completeness of restricted uniform linear formula classes w.r.t. SATand the existence of unsatisfiable uniform linear witne...

Rule induction systems seek to generate rule sets which are optimal in the complexity of the rule set. This paper develops a formal proof of the NP-Completeness of the problem of generating the simplest rule set (MIN RS) which accurately predicts examples in the training set for a particular type of generalization algorithm algorithm and complexity measure. The proof is then informally extended...

The computational complexity of the partition, 0-1 subset sum, unbounded subset sum, 0-1 knapsack and unbounded knapsack problems and their multiple variants were studied in numerous papers in the past where all the weights and profits were assumed to be integers. We re-examine here the computational complexity of all these problems in the setting where the weights and profits are allowed to be...

This is the fourth edition of a quarterly column the purpose of which is to provide continuing coverage of new developments in the theory of NP-completeness. The presentation is modeled on that used by by M. R. Garey and myself in our book ‘‘Computers and Intractability: A Guide to the Theory of NP-Completeness,’’ W. H. Freeman & Co., San Francisco, 1979 (hereinafter referred to as ‘‘[G&J]’’; p...

This is the final article in a series of four articles. Richard Karp has proven that a deterministic polynomial time solution to K-SAT will result in a deterministic polynomial time solution to all NP-Complete problems. However, it is demonstrated that a deterministic polynomial time solution to any NP-Complete problem does not necessarily produce a deterministic polynomial time solution to all...