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- Alberto Caprara
- RECOMB
- 1997

We prove that the problem of sorting a permutation by the minimum number of reversals is NP-hard, thus answering a major question on the complexity of a problem which has widely been studied in the last years. The proof is based on the strong relationship between this problem and the problem of finding the maximum number of edge-disjoint alternating cycles… (More)

- Alberto Caprara, Matteo Fischetti, Paolo Toth
- Operations Research
- 1999

We present a Lagrangian-based heuristic for the well-known Set Covering Problem (SCP). The algorithm was initially designed for solving very large scale SCP instances, involving up to 5,000 rows and 1,000,000 columns, arising from crew scheduling in the Italian Railway Company, Ferrovie dello Stato SpA. In 1994 Ferrovie dello Stato SpA, jointly with the… (More)

- Alberto Caprara
- SIAM J. Discrete Math.
- 1999

We analyze the strong relationship among three combinatorial problems, namely, the problem of sorting a permutation by the minimum number of reversals (MIN-SBR), the problem of finding the maximum number of edge-disjoint alternating cycles in a breakpoint graph associated with a given permutation (MAX-ACD), and the problem of partitioning the edge set of an… (More)

- Alberto Caprara, Matteo Fischetti
- Math. Program.
- 1996

Given the integer polyhedron P I := convfx 2 Z n : Ax bg, w h e r e A 2 Z mn and b 2 Z m , a Chvv atal-Gomory (CG) cut is a valid inequality f o r P I of the type T Ax b T bc for some 2 R m + such that T A 2 Z n. In this paper we study f0 1 2 g-CG cuts, arising for 2 f 0 1=2g m. W e show that the associated separation problem, f0 1 2 g-SEP, i s e q u i v… (More)

- Alberto Caprara
- INFORMS Journal on Computing
- 2003

- Alberto Caprara, Paolo Toth, Matteo Fischetti
- Annals OR
- 2000

The Set Covering Problem (SCP) is a main model for several important applications, including crew scheduling in railway and mass-transit companies. In this survey, w e focus our attention on the most recent and eeective algorithms for SCP, considering both heuristic and exact approaches, outlining their main characteristics and presenting an experimental… (More)

- Alberto Caprara, Matteo Fischetti, Paolo Toth
- Operations Research
- 2002

- Alberto Caprara, David Pisinger, Paolo Toth
- INFORMS Journal on Computing
- 1999

The Quadratic Knapsack Problem (QKP) calls for maximizing a quadratic objective function subject to a knapsack constraint, where all coeecients are assumed to be nonnegative and all variables are binary. The problem has applications in location and hydrology, and generalizes the problem of checking whether a graph contains a clique of a given size. We… (More)

- Alberto Caprara
- FOCS
- 2002

- Alberto Caprara, Hans Kellerer, Ulrich Pferschy, David Pisinger
- European Journal of Operational Research
- 2000

We address a variant of the classical knapsack problem in which an upper bound is imposed on the number of items that can be selected. This problem arises in the solution of real-life cutting stock problems by column generation, and may be used to separate cover inequalities with small support within cutting plane approaches to integer linear programs. We… (More)