it Dor

Graph Decomposition is NP-Complete: A Complete Proof of Holyer's Conjecture

An H-decomposition of a graph G=(V,E) is a partition of E into subgraphs isomorphic to H. Given a fixed graph H, the H-decomposition problem is to determine whether an input graph G admits an H-decomposition. In 1980, Holyer conjectured that H-decomposition is NP-complete whenever H is connected and has three edges or more. Some partial results have been obtained since then. A complete proof of Holyers conjecture is the content of this paper. The characterization problem of all graphs H for which H-decomposition is NP-complete is hence reduced to graphs where every connected component contains at most two edges.

Selecting the Median

Improving a long-standing result of Schonhage, Paterson, and Pippenger [ J. Comput. System Sci., 13 (1976), pp. 184--199] we show that the median of a set containing

SOKOBAN and other motion planning problems

n

Graph decomposition is NPC - a complete proof of Holyer's conjecture

elements can always be found using at most

Geometric pattern matching in d-dimensional space

c \cdot n

Median Selection Requires

comparisons, where c<2.95.

(2+\epsilon)n

Abstract We consider a natural family of motion planning problems with movable obstacles and obtain hardness results for them. Some members of the family are shown to be PSPACE-complete thus improving and extending (and also simplifying) a previous NP-hardness result of Wilfong. The family considered includes a motion planning problem which forms the basis of a popular computer game called SOKOBAN. The decision problem corresponding to SOKOBAN is shown to be NP-hard. The motion planning problems considered are related to the “warehousemans problem” considered by Hopcroft, Schwartz and Sharir, and to geometric versions of the motion planning problem on graphs considered by Papadimitriou, Raghavan, Sudan and Tamaki.

Comparisons

An H-decomposition of a graph G = (V,E) is a partition of E into subgraphs isomorphic to H. Given a fixed graph H, the H-decomposition problem is to determine whether an input graph G admits an H-decomposition. I. Holyer (1980) conjectured that H-decomposition is Np-complete whenever H is connected and has at least 3 edges. Some partial results have been obtained during the last decade. A complete proof for Holyers conjecture is the content of this paper.

Geometric Pattern Matching in d-Dimensional Space

Abstract. We show that, using the L∞ metric, the minimum Hausdorff distance under translation between two point sets of cardinality n in d -dimensional space can be computed in time O(n(4d-2)/3 log2n) for 3 < d

Median selection requires (2+/spl epsiv/)n comparisons

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