Computing Small Search Numbers in Linear Time

Let G = V; E be a graph. The linear-width of G is de ned as the smallest integer k such that E can be arranged in a linear ordering e1; : : : ; er such that for every i = 1; : : : ; r ,1, there are at most k vertices both incident to an edge that belongs to fe1; : : : ; eig as to an edge that belongs to fei+1; : : : ; erg. For each xed constant k, a linear time algorithm is given, that decides for any graph G = V; E whether the linear-width of G is at most k, and if so, nds the corresponding ordering of E. Linear-width has been proven to be related with the following graph searching parameters: mixed search number, node search number, and edge search number. A consequence of this is that we obtain for xed k, linear time algorithms that check whether a given graph can be mixed, node, or edge searched with at most k searchers, and if so, output the corresponding search strategies.

• Type: Conference
• Year: 2004
• Where: IWPEC
• Authors: Hans L. Bodlaender, Dimitrios M. Thilikos
• Keywords: Edge, IWPEC 2004, Linear Time Algorithms, Search Number