Doctoral School on Engineering Sciences Università Politecnica delle Marche Extended summary Finding special structures in Integer Linear Programming problems Curriculum: Ingegneria informatica, gestionale e dell'Automazione Author Angelo Parente Tutor Fabrizio Marinelli Date: 15-02-2013 _______________________________________________________________________________________________________________ Abstract. In general, Integer Linear Programming problems are computationally hard to solve. The de- sign of efficient algorithms for them often takes advantage from the analysis of the problem un- derlying mathematical structure. Starting from the problem of finding the maximum embedded reflected network submatrix of a matrix with entries in  , this work deals with the equivalent problem of finding the maximum balanced induced subgraph of a signed graph (MBS, Max Bal- anced Subgraph). The contribution is twofold. In the first part of the work, a new heuristic for the MBS problem, the Cycle-Contraction Heuristic (CCH), has been proposed. The algorithm is based on a graph transformation rule that progressively reduces the lengths of cycles, preserving at the same time the feasibility of solutions for the MBS problem. CCH turns out to be more ef- fective of the state-of-the-art heuristics. The efficiency and the effectiveness of CCH can be fur- ther improved by means of new rules of data reduction, i.e., by a procedure that simplifies instances and/or decrease their size while preserving the optimal solution of the problem. In the second part of the work, a new exact approach for the MBS problem has been pro- posed. Such method is based on a polynomial transformation rule that turns a signed graphs into a simple 2-layer graph. The transformation establishes a strong connection between MBS and the