## Efficient enumeration of all minimal separators in a graph

##### Author(s)

Shen, Hong

Liang, W.

##### Griffith University Author(s)

##### Year published

1997

##### Metadata

Show full item record##### Abstract

This paper presents an efficient algorithm for enumerating all minimal a-b separators separat- ing given non-adjacent vertices a and b in an undirected connected simple graph G = (V,E). Our algorithm requires O(n3R,b) time, which improves the known result of 0(n4R,b) time for solving this problem, where |V| = n and R(ab) is the number of minimal a-b separators. The algorithm can be generalized for enumerating all minimal A-B separators that separate non-adjacent vertex sets A,B < V, and it requires O(n2(n - no - nB)R(AB)) time in this case, where n(a) = |A|, n(b) = |B| and r(ab) is the number of all minimal A-B separators. ...

View more >This paper presents an efficient algorithm for enumerating all minimal a-b separators separat- ing given non-adjacent vertices a and b in an undirected connected simple graph G = (V,E). Our algorithm requires O(n3R,b) time, which improves the known result of 0(n4R,b) time for solving this problem, where |V| = n and R(ab) is the number of minimal a-b separators. The algorithm can be generalized for enumerating all minimal A-B separators that separate non-adjacent vertex sets A,B < V, and it requires O(n2(n - no - nB)R(AB)) time in this case, where n(a) = |A|, n(b) = |B| and r(ab) is the number of all minimal A-B separators. Using the algorithm above as a routine, an efficient algorithm for enumerating all minimal separators of G separating G into at least two connected components is constructed.

View less >

View more >This paper presents an efficient algorithm for enumerating all minimal a-b separators separat- ing given non-adjacent vertices a and b in an undirected connected simple graph G = (V,E). Our algorithm requires O(n3R,b) time, which improves the known result of 0(n4R,b) time for solving this problem, where |V| = n and R(ab) is the number of minimal a-b separators. The algorithm can be generalized for enumerating all minimal A-B separators that separate non-adjacent vertex sets A,B < V, and it requires O(n2(n - no - nB)R(AB)) time in this case, where n(a) = |A|, n(b) = |B| and r(ab) is the number of all minimal A-B separators. Using the algorithm above as a routine, an efficient algorithm for enumerating all minimal separators of G separating G into at least two connected components is constructed.

View less >

##### Journal Title

Theoretical Computer Science

##### Volume

180

##### Issue

1-2

##### Subject

Mathematical Sciences

Information and Computing Sciences