On the approximability of comparing genomes with duplicates.
We show that some classical P-complete problems can be solved efficiently in average NC. The probabilistic model we consider is the sample space of input descriptions of the problem with the underlying distribution being the uniform one. We present parallel algorithms that use a polynomial number of processors and have expected time upper bounded by (e ln 4 + o(1))log n, asymptotically with high probability, where n is the instance size.
In the literature various types of restarting automata have been studied that are based on contextual rewriting. A word w is accepted by such an automaton if, starting from the initial configuration that corresponds to input w, the word w is reduced to the empty word by a finite number of applications of these contextual rewritings. This approach is reminiscent of the notion of McNaughton families of languages. Here we put the aforementioned types of restarting automata into the context of McNaughton...
Simple games cover voting systems in which a single alternative, such as a bill or an amendment, is pitted against the status quo. A simple game or a yes-no voting system is a set of rules that specifies exactly which collections of “yea” votes yield passage of the issue at hand. Each of these collections of “yea” voters forms a winning coalition. We are interested in performing a complexity analysis on problems defined on such families of games. This analysis as usual depends on the game representation...
Simple games cover voting systems in which a single alternative, such as a bill or an amendment, is pitted against the status quo. A simple game or a yes-no voting system is a set of rules that specifies exactly which collections of “yea” votes yield passage of the issue at hand. Each of these collections of “yea” voters forms a winning coalition. We are interested in performing a complexity analysis on problems defined on such families of games....
We show that the decision problem for p-reinforcement, p-total rein- forcement, total restrained reinforcement, and k-rainbow reinforcement are NP-hard for bipartite graphs.