Abstract
We investigate various problems related to circulant graphs — finding the shortest path between two vertices, finding the shortest loop, and computing the diameter. These problems are related to shortest vector problems in a special class of lattices. We give matching upper and lower bounds on the length of the shortest loop. We claim NP-hardness results, and establish a worst-case/average-case connection for the shortest loop problem. A pseudo-polynomial time algorithm for these problems is also given. Our main tools are results and methods from the geometry of numbers.
Supported in part by NSF grant CCR-9634665 and a J. S. Guggenheim Fellowship.
Supported in part by ARC grants A49702337 and A49801415.
Supported in part by NSF grant CCR-9634665.
Supported in part by ARC grant A69700294.
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Cai, JY., Havas, G., Mans, B., Nerurkar, A., Seifert, JP., Shparlinski, I. (1999). On Routing in Circulant Graphs. In: Asano, T., Imai, H., Lee, D.T., Nakano, Si., Tokuyama, T. (eds) Computing and Combinatorics. COCOON 1999. Lecture Notes in Computer Science, vol 1627. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48686-0_36
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DOI: https://doi.org/10.1007/3-540-48686-0_36
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