Exact and heuristic algorithms for the maximum weighted submatrix coverage problem

The maximum weighted submatrix coverage problem is a recently introduced with applications in data mining. It concerned selecting K submatrices of given numerical matrix such that the sum matrix-entries, which occur at least one selected submatrices, maximized. In paper introducing problem, problem-specific constraint programming approach was developed and embedded large neighborhood-search to obtain heuristic. A compact integer linear formulation also presented, but deemed inefficient due its size. this paper, we introduce new formulations for them based on Benders decomposition. obtained decomposition-based has nice combinatorial structure, i.e., there no need solve programs separate cuts. We present preprocessing procedures valid inequalities all formulations. develop greedy randomized adaptive search procedure enhanced local search. computational study using instances from literature done evaluate effectiveness our approaches. Our algorithms manage find improved primal solutions ten out 17 real-world instances, optimality proven two instances. Moreover, over 700 1617 large-scale synthetic compared heuristics literature.