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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-time algorithm is known for it. The naive deterministic algorithm for this problem runs in time 3^n, up to polynomial factors. In this paper, we design an exact deterministic algorithm for this problem running in time 2.9416^n. Thus, our algorithm can handle problem instances of larger size than the naive algorithm in the same amount of time. We also present another deterministic and a randomized algorithm for this problem that both have an even better performance for graphs with small maximum degree.
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
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
Consider the problem of determining whether there exists a spanning hypertree in a given k-uniform hypergraph. This problem is trivially in P for k=2, and is NP-complete for k>= 4, whereas for k=3, there exists a polynomial-time algorithm based on Lo