One fundamental problem in image recognition is to establish the resemblance of two images. This can be done by searching the best pixel to pixel mapping taking into account monotonicity and continuity constraints. We show that this problem is NPcomplete by reduction from 3-SAT, thus giving evidence that the known exponential time algorithms are justified, but approximation algorithms or simpli...

When can t terminal pairs in an m× n grid be connected by t vertex-disjoint paths that cover all vertices of the grid? We prove that this problem is NP-complete. Our hardness result can be compared to two previous NP-hardness proofs: Lynch’s 1975 proof without the “cover all vertices” constraint, and Kotsuma and Takenaga’s 2010 proof when the paths are restricted to have the fewest possible cor...

The Lambek-Grishin calculus LG is the symmetric extension of the non-associative Lambek calculus NL. In this paper we prove that the derivability problem for LG is NP-complete.

We consider a robotic owshop model in which a single robot is responsible for the transportation of parts between machines and the amount of time that a part spends on a machine must be comprised in some prede ned interval. The objective is to nd a feasible schedule with minimal cycle time. Many researchers have proposed nonpolynomial solution methods for a variety of closely related robotic ow...

We present a new optical method for solving bounded (input-length-restricted) NP-complete combinatorial problems. We have chosen to demonstrate the method with an NP-complete problem called the traveling salesman problem (TSP). The power of optics in this method is realized by using a fast matrix-vector multiplication between a binary matrix, representing all feasible TSP tours, and a gray-scal...

Distance labeling is a preprocessing technique introduced by Peleg [Journal of Graph Theory, 33(3)] to speed up distance queries in large networks. Herein, each vertex receives a (short) label and, the distance between two vertices can be inferred from their two labels. One such preprocessing problem occurs in the hub labeling algorithm [Abraham et al., SODA’10]: the label of a vertex v is a se...

Let G be a simple, undirected graph. We say that two edges of G are within distance 2 of each other if either they are adjacent or there is some other edge that is adjacent to both of them. A distance-2-edge-coloring of G is an assignment of colors to edges so that any two edges within distance 2 of each other have distinct colors, or equivalently, a vertex-coloring of the square of the line gr...

A polynomial algorithm for solving the ”Hamiltonian circuit” problem is presented in the paper. Computational complexity of the algorithm is equal to O ( n log 2 n ) where n is the cardinality of the observed graph vertex set. Thus the polynomial solvability for NP -complete problems is proved.

Under the assumption that NP does not have p-measure 0, we investigate reductions to NP-complete sets and prove the following: 1. Adaptive reductions are more powerful than nonadaptive reductions: there is a problem that is Turing-complete for NP but not truth-table-complete. 2. Strong nondeterministic reductions are more powerful than deterministic reductions: there is a problem that is SNP-co...

Two graphs G and G' are said to be k-isomorphic if their edge sets can be partitioned into E(G) = ElUE2 u . . . uEk and E(G' > = E-j-U E; IJ l . . IJEk such that as graphs, E i and E! are 1 isomorphic for l<i<k. In this note we show that it is NP-complete to decide whether two graphs are 2-isomorphic. This research was supported in part by National Science Foundation grant MCS77-05313. -I * Giv...