On Routing in Circulant Graphs

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 NPhardness 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.

• Type: Conference
• Year: 1999
• Where: COCOON
• Authors: Jin-yi Cai, George Havas, Bernard Mans, Ajay Nerurkar, Jean-Pierre Seifert, Igor Shparlinski
• Keywords: COCOON 1999, Combinatorics, Shortest Loop, Shortest Loop Problem, Shortest Path