Minimum Link Flow Problem and Its Solution With Sparse Modeling

Recently, a statistical modeling approach called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sparse modeling</i> has attracted much attention, especially in the fields of signal and image processing. Sparse modeling is applicable to solve problems in a variety of fields, and a few applications have begun to be explored in the field of information networking. Sparse modeling is expected to be applicable to many information networking problems, but it has not yet been well investigated. In this study, we examine how sparse modeling can be applied to solve a new network flow problem called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">minimum link flow problem</i>. The minimum link flow problem, which includes problems such as the minimum cost flow problem and the minimum Steiner tree problem under certain conditions, is a combinatorial optimization problem, and to the best of our knowledge, no effective solution has been proposed for the minimum link flow problem. In this study, we formulate the minimum link flow problem using sparse modeling and propose a greedy algorithm called Constrained Orthogonal Matching Pursuit (COMP), which imposes both upper and lower bounds on the solution. Through various experiments, we investigate how effectively the COMP can solve the minimum link flow problem. Our findings include that COMP can solve the minimum link flow problem with multiple sources and sinks 1.1–1.3 times more effectively than benchmark conventional methods.