Solving Generalized Maximum-Weight Connected Subgraph Problem for Network Enrichment Analysis

Abstract

Abstract. Network enrichment analysis methods allow to identify active modules without being biased towards a priori defined pathways. One of mathematical formulations of such analysis is a reduction to a maximum-weight connected subgraph problem. In particular, in analysis of metabolic networks a generalized maximum-weight connected subgraph (GMWCS) problem, where both nodes and edges are scored, naturally arises. Here we present the first to our knowledge practical exact GMWCS solver. We have tested it on real-world instances and compared to similar solvers. First, the results show that on node-weighted instances GMWCS solver has a similar performance to the best solver for that problem. Second, GMWCS solver is faster compared to the closest analogue when run on GMWCS instances with edge weights.

Reduction techniques for the prize collecting Steiner tree problem and the maximum‐weight connected subgraph problem

“…Finally, the NV/SL and the NTD 3 tests are both notably fast, but while the NV/SL test is able to reduce the number of vertices by more than 15% and the number of edges by more than 10%, NTD 3 is the least effective of all reduction methods. However, it should be noted that the reduction methods described in this article usually become more effective in combination, [27]. since eliminations performed after the execution of a specific reduction method often set the stage for renewed reductions by this method.…”

“…This section provides computational results of the MWCSP reduction package introduced in this article on three test sets described in Table 5. The ACTMOD and JMPALMK instances were all solved to optimality in the course of the 11th DIMACS Challenge, while the SHINY test set has only been recently introduced [27].…”

“…Finally, all SHINY test instances can be solved in less than second-with an average of less than 0.1 seconds. In particular the 25e814a792c4 instance could not be solved by the approach described in [27], but can be solved by our reduction techniques in less than 0.1 seconds with an objective value of 1083.308.…”

Ranking Vertices for Active Module Recovery Problem

“…A parameter of this procedure is how to select set X. For this end, similarly to the first step, we solve an MWCS instance, but with an additional constraint that requires the solution to contain at least one vertex from R and at least one but not all vertices from C. We set X as an intersection of the solution and the set C. The corresponding instance is solved by a modified solver from [9], where corresponding constraints were added into the ILP formulation.…”

Combinatorial Detection of Conserved Alteration Patterns for Identifying Cancer Subnetworks

“…within a molecular interaction network with speci c characteristics, e.g. the subnetwork of a xed size with the highest total "weight" [16,17] or the subnetwork seeded by a particular node that can be derived through a di usion process [18,19]; naturally these methods do not capture recurrent alteration patterns across a cohort. A direction particularly relevant to our paper is motivated by a number of related works [18,20,21,22], and explored by Bomersbach et al [23], which suggests to nd a subnetwork of a given size k with the goal of maximizing h, the number of samples for which at least one gene of the subnetwork is in an altered state.…”