Abstract
A toroidal periodic graph G α is defined by a positive integer vector α and a directed graph G in which the edges are associated with integer vectors. G α has a vertex (v, y) for each vertex v of G and each integer vector \(\vec 0 \le y < \alpha \). G α has an edge from (v, y) to (w, z) if and only if G has an edge from v to w associated with t, and z = y+t mod α.
We show that path problems for toroidal periodic graphs G α can be solved in polynomial time if G has a constant number of strongly connected components. The general path problem in toroidal periodic graphs is shown to be NP-complete for all \(\alpha \ge \vec 2\). Additionally, we present a procedure for determining the number of strongly connected components in a toroidal periodic graph. This procedure takes polynomial time for all instances G and α.
The introduced methods are very general and can also be used to solve further graph problems in polynomial time on even more general toroidal periodic graphs.
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© 1994 Springer-Verlag Berlin Heidelberg
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Höfting, F., Wanke, E. (1994). Polynomial time analysis of toroidal periodic graphs. In: Abiteboul, S., Shamir, E. (eds) Automata, Languages and Programming. ICALP 1994. Lecture Notes in Computer Science, vol 820. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58201-0_97
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DOI: https://doi.org/10.1007/3-540-58201-0_97
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