Pushing blocks is hard

Pushing blocks is hard

We prove NP-hardness of a wide class of pushing-block puzzles similar to the classic Sokoban, generalizing several previous results [5, 6, 9, 10, 15, 17]. The puzzles consist of unit square blocks on an integer lattice; all blocks are movable. The robot may move horizontally and vertically in order to reach a specified goal position. The puzzle variants differ in the number of blocks that the r...

Pushing blocks is np-complete for noncrossing solution paths

Testing perfection is hard

A graph property P is strongly testable if for every fixed > 0 there is a one-sided -tester for P whose query complexity is bounded by a function of . In classifying the strongly testable graph properties, the first author and Shapira showed that any hereditary graph property (such as P the family of perfect graphs) is strongly testable. A property is easily testable if it is strongly testable ...

Box Pleating is Hard

In their seminal 1996 paper, Bern and Hayes initiated investigation into the computational complexity of origami [3]. They proved that it is NP-hard to determine whether a given general crease pattern can be folded flat, when the creases have or have not been assigned crease directions (mountain fold or valley fold). Since that time, there has been considerable work in analyzing the computation...

Axiom Pinpointing is Hard

We investigate the complexity of several decision, enumeration and counting problems in axiom pinpointing in Description Logics. We prove hardness results that already hold for the propositional Horn fragment. We show that for this fragment, unless p = np, all minimal subsets of a given TBox that have a given consequence, i.e. MinAs, cannot be enumerated in a specified lexicographic order with ...