Finding Isolated Cliques by Queries -- An Approach to Fault Diagnosis with Many Faults

A well-studied problem in fault diagnosis is to identify the set of all good processors in a given set {p1, p2, . . . , pn} of processors via asking some processors pi to test whether processor pj is good or faulty. Mathematically, the set C of the indices of good processors forms an isolated clique in the graph with the edges E = {(i, j) : if you ask pi to test pj then pi states that "pj is good"}; where C is an isolated clique iff it holds for every i C and j = i that (i, j) E iff j C. In the present work, the classical setting of fault diagnosis is modified by no longer requiring that C contains at least n+1 2 of the n nodes of the graph. Instead, one is given a lower bound a on the size of C and the number n of nodes and one has to find a list of up to n/a candidates containing all isolated cliques of size a or more where the number of queries whether a given edge is in E is as small as possible. It is shown that the number of queries necessary differs at most by n for...

• Type: Conference
• Year: 2004
• Where: DAGSTUHL
• Authors: William I. Gasarch, Frank Stephan
• Keywords: DAGSTUHL 2004, DAGSTUHL 2007, Fault Diagnosis, Isolated Cliques, Well-studied Problem