M. Burmester, Y. Desmedt, and Y. Wang. Using approximation hardness to achieve dependable computation. In: Proc. the 2nd International Conference on Randomization and Approximation Techniques in Computer Science, RANDOM '98. Lecture Notes in Computer Science, Springer Verlag, 1998.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....graph G(V# , V# , INPUT, output; E) a set U is called a set of strictly critical vertices of G if, for any solution graph P in G, P passes through at least one vertex of U . Note that a set of strictly critical vertices is di#erent from a vertex separator (though related) defined in [3]. SCV (i.e. Strictly Critical Vertices) Instance: An AND OR graph G(V# , V# , INPUT, output; E) and a positive integer k # (V# # # output ) Question: Does there exist a size k set of strictly critical vertices Theorem 5. SCV is NP complete. Proof. We first show that SCV NP. It ....

M. Burmester, Y. Desmedt, and Y. Wang. Using approximation hardness to achieve dependable computation. In: Proc. the 2nd International Conference on Randomization and Approximation Techniques in Computer Science, RANDOM '98. Lecture Notes in Computer Science, Springer Verlag, 1998.

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Burmester, M. and Desmedt, Y. and Wang, Y.: Using approximation hardness to achieve dependable computation. In: Proceedings of Second International Conference on Randomization and Approximation Techniques in Computer Science, Lecture Notes in Computer Science 1518, Springer Verlag, 1998, 172--186.

....power is polynomial time bounded) for k = cn, where c 1 is any given constant. This result improves a great deal on the results of Franklin and Wright [6] which are for unconditional reliability) To achieve this improvement we use some of the hardness results of Burmester, Desmedt, and Wang in [3]. The idea underlying our construction is that we will design strongly n connected communication graphs in such a way that it is hard for the adversary to find the neighborhood disjoint n paths which is a witness to the strong n connectivity. Hence the adversary does not know which processors ....

....u and v have no common neighbor in f(GI) if and only if (u; v) 2 EG . Hence there is a neighborhood independent set of size n in G if and only if there is an independent set of size n in GI. ut The following results follow directly from the corresponding results in Burmester, Desmedt, and Wang [3]. Theorem 2. 3] There is a constant 0 such that it is NP hard to compute a vertex set V 0 V of a graph G(V; E) with the following properties: 1. jV 0 j nm , where n is the size of the maximum neighborhood independent set of G and m = jV j. 2. V 0 contains a neighborhood ....

[Article contains additional citation context not shown here]

M. Burmester, Y. Desmedt, and Y. Wang. Using approximation hardness to achieve dependable computation. In: Proc. of the Second International Conference on Randomization and Approximation Techniques in Computer Science, LNCS 1518, pages 172--186, Springer Verlag, 1998.

....power is polynomial time bounded) for k = cn, where c 1 is any given constant. This result improves a great deal on the results of Franklin and Wright [6] which are for unconditional reliability) To achieve this improvement we use some of the hardness results of Burmester, Desmedt, and Wang in [3]. The idea underlying our construction is that we will design strongly n connected communication graphs in such a way that it is hard for the adversary to find the neighborhood disjoint n paths which is a witness to the strong n connectivity. Hence the adversary does not know which processors ....

....neighbor in f(G) if and only if (u; v) 2 E. Hence there is a neighborhood independent set of size n in GNI if and only if there is an independent set of size n in G. ut The following results follow directly from the corresponding results for independent sets in Burmester, Desmedt, and Wang [3]. Theorem 2. 3] There is a constant 0 such that it is NP hard to compute a vertex set V 0 V of a graph G(V; E) with the following properties: 1. jV 0 j nm , where n is the size of the maximum neighborhood independent set of G and m = jV j. 2. V 0 contains a neighborhood ....

[Article contains additional citation context not shown here]

M. Burmester, Y. Desmedt, and Y. Wang. Using approximation hardness to achieve dependable computation. In: Proc. of the Second International Conference on Randomization and Approximation Techniques in Computer Science, LNCS 1518, pages 172--186, Springer Verlag, 1998.

....to decide whether a given multicast graph is strongly k connected. Proof. It is clear that the specified problem is in NP. Whence it suffices to reduce the following NP complete problem IS (Independent Set) to our problem. A similar reduction has appeared in Burmester, Desmedt, and Wang [3]. The independent set problem is: Instance: A graph G(V; E) and a number k. Question: Does there exist a node set V 1 V of size k such that any two nodes in V 1 are not connected by an edge in E The input G(VG ; EG ) to IS, consists of a set of vertices VG = fv 1 ; vn g and a set ....

M. Burmester, Y. Desmedt, and Y. Wang. Using approximation hardness to achieve dependable computation. In: Proc. of the Second International Conference on Randomization and Approximation Techniques in Computer Science, LNCS 1518, pages 172--186, Springer Verlag, 1998.

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