Space-optimal, backtracking algorithms to list the minimal vertex separators of a graph

Abstract

For a graph G in read-only memory on n vertices and m edges and a write-only output buffer, we give two algorithms using only O ( n ) rewritable space. The first algorithm lists all minimal a − b separators of G with a polynomial delay of O ( n m ) . The second lists all minimal vertex separators of G with a cumulative polynomial delay of O ( n 3 m ) . One consequence is that the algorithms can list the minimal a − b separators (and minimal vertex separators) spending O ( n m ) time (respectively, O ( n 3 m ) time) per object output.