| Æ¡Æ¡The concept of profile, together with bandwidth, originates from handling sparse matrices in solving linear systems of equations. The problem can be re-formulated in term of graphs as follows. Given a graph G=(V,E) of n vertices, the profile minimization problem is to find a one-to-one mapping from V onto {1,2,...,n} such that \sum{w(v): v in V} is as small as possible, where w(v) is the maximum of f(v)-f(x) with x taking over all neighbors of v and v itself. The problem has several equivalent definitions including interval graph completion and graph searching. The purpose of this talk is to survey the problem. If time is enough, we will also discuss related problems of bandwidth and bandwidth sum. |