# The complexity of path problems in graphs and path systems of bounded bandwidth

## Abstract

The graph accessibility problem (GAP), the solvable path system problem (SPS), and the and/or graph accessibility problem (AGAP) restricted to graphs or path systems of bandwidth S(n), for some function S on the natural numbers, are considered. These problems are denoted by GAP(S(n)), SPS(S(n)), and AGAP(S(n)), respectively. The monotone and acyclic versions of AGAP(S(n)) are also considered, denoted by \(AGA\vec P\) (S(n)) and AAGAP(S(n)), respectively. It is shown that AGAP(S(n)) and SPS(S(n)) are equivalent via log space reductions for finite-degree graphs and path systems. (This equivalence is also valid for montone graphs and path systems.) It is also shown that AAGAP(S(n)) is in NTISP(poly,S(n)), i.e. the class of problems solvable by nondeterministic algorithms in polynomial time and simultaneous S(n) Space. Previous results that show GAP(S(n)) ε DSPACE (log S(n) × log n) and AGAP(S(n)) ε DSPACE(S(n) × log n) are surveyed. (It is known, also, that \(AGA\vec P\) (S(n)) is in DTISP(poly,S(n)) and, in fact, is log space complete for this class.)

## Keywords

Turing Machine Black Marker White Marker Path System Pebble Game## Preview

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