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The 3-domatic number problem asks whether a given graph can be partitioned intothree dominating sets. We prove that this problem can be solved by a deterministic algorithm in time 2.695^n (up to polynomial factors). This result improves the previous bound of 2.8805^n, which is due to Fomin, Grandoni, Pyatkin, and Stepanov. To prove our result, we combine an algorithm by Fomin et al. with Yamamotos algorithm for the satisfiability problem. In addition, we show that the 3-domatic number problem can be solved for graphs G with bounded maximum degree Delta(G) by a randomized algorithm, whose running time is better than the previous bound due to Riege and Rothe whenever Delta(G) >= 5. Our new randomized algorithm employs Schoenings approach to constraint satisfaction problems.
The three domatic number problem asks whether a given undirected graph can be partitioned into at least three dominating sets, i.e., sets whose closed neighborhood equals the vertex set of the graph. Since this problem is NP-complete, no polynomial-t
In this paper, we study the properties of the Frank-Wolfe algorithm to solve the ExactSparse reconstruction problem. We prove that when the dictionary is quasi-incoherent, at each iteration, the Frank-Wolfe algorithm picks up an atom indexed by the s
One of the strongest techniques available for showing lower bounds on quantum communication complexity is the logarithm of the approximation rank of the communication matrix--the minimum rank of a matrix which is entrywise close to the communication
We present an exact dynamical QCD simulation algorithm for the $O(a)$-improved Wilson fermion with odd number of flavors. Our algorithm is an extension of the non-Hermitian polynomials HMC algorithm proposed by Takaishi and de Forcrand previously. In