A. Caprara, D. Pisinger, P. Toth. Exact solution of the Quadratic Knapsack Problem. INFORMS Journal on Computing, 11:125-137, 1999. Home/Search Document Details and Download
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Structural Alignment of Large-Size Proteins via Lagrangian.. - Caprara, Lancia (2002) (Correct)
....Lagrangian Relaxation techniques are used for an alignment algorithm of any type. The algorithm we propose is based on a similar approach which was successfully used for other Binary Quadratic Programming problems, such as the Quadratic Assignment Problem [7] or the Quadratic Knapsack Problem [6]. These problems bear many similarities with the structure alignment problem. In particular, there are pro ts p ij in the objective function which are attained when two binary variables x i and x j are both set to 1 in a solution. Analogously, in the alignment problem, we may have a pro t in ....
.... that the problem obtained by removing constraints (10) is as dicult as the maximization of a linear function subject to (2) or, equivalently, 3) and (4) This property is common to other binary quadratic programs, such as the Quadratic Assignment Problem [7] and the Quadratic Knapsack Problem [6]. Below, we illustrate the situation in detail for our problem. 2.2 Decomposition andLagrangian relaxation Proposition 1. The problem de ned by (7) 8) 9) and (11) can be solved in O(jE1 jjE2 j) time. Proof. After the removal of equations (10) each variable ylm appears only in the ....
A. Caprara, D. Pisinger and P. Toth, Exact Solution of the Quadratic Knapsack Problem, INFORMS J. on Comput., 11 (1999) 125-137.
A Semidefinite Programming Approach to the Quadratic.. - Helmberg, Rendl.. (2000) (3 citations) (Correct)
....programming, e.g. in VLSI and compiler design [10, 21] Current practical approaches for solving (QK) are branch and bound algorithms. The bounds are specially designed for the quadratic knapsack problem and often require special properties of the objective function such as nonnegativity of c ij [14, 6]. These approaches are of little use if (QK) appears as a subproblem within general constrained quadratic 0 1 programming. This drawback can be overcome by resorting to a polyhedral approach. Typically, polyhedral methods work with linear relaxations of (QK) However, these often exhibit a large ....
A. CAPRARA, D. PISINGER, and P. TOTH. Exact solution of quadratic knapsack problems. INFORMS J. on Comput., 11(2):125-137, 1999.
Discrete Location Problems With Push-Pull Objectives - Krarup, Pisinger, Plastria (1999) Self-citation (Pisinger) (Correct)
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A. Caprara, D. Pisinger, P. Toth (1999), \Exact Solution of the Quadratic Knapsack Problem", INFORMS Journal on Computing 11, 125-137.
Exact Solution of P-Dispersion Problems - Pisinger (1999) Self-citation (Pisinger) (Correct)
....d ij = 1 iff the edge (i; j) 2 E. In the more general quadratic knapsack problem (QKP) each facility has an associated weight w i and the problem is to maximize the overall distance sum between established facilities subject to an upper limit c on the applied weights. Caprara, Pisinger, Toth [2] prsented an exact 2 algorithm for this problem based on branch and bound where tight bounds are found through a reformulation. The present paper relies in a large extent on the techniques developed for the QKP. In the present paper, we are however able to derive a reformulation scheme which runs ....
....found through a reformulation. The present paper relies in a large extent on the techniques developed for the QKP. In the present paper, we are however able to derive a reformulation scheme which runs in polynomial time O(n 3 ) as opposed to the subgradient optimization algorithm presented in [2]. Also, the time bounds for deriving upper bounds are tighter for the p dispersion sum problem than for the QKP. In the sequel we consider the most general case of p dispersion problems, where the distances d ij do not need to satisfy the triangle inequality and in particular they may take on ....
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A. Caprara, D. Pisinger, P. Toth (1999), "Exact solution of the quadratic knapsack problem ", INFORMS Journal on Computing, 11, 125--137.
Cost based Filtering for the - Constrained Knapsack Problem (Correct)
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A. Caprara, D. Pisinger, P. Toth. Exact solution of the Quadratic Knapsack Problem. INFORMS Journal on Computing, 11:125-137, 1999.
Simple and Fast: Improving a Branch-and-Bound Algorithm for.. - Fahle (2002) (4 citations) (Correct)
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A. Caprara and D. Pisinger and P. Toth. Exact Solutions on the Quadratic Knapsack Problem. Informs Journal on Computing, 11(2):125--137, 1999.
Cost Based Filtering vs. Upper Bounds for Maximum Clique - Fahle (2002) (Correct)
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A. Caprara and D. Pisinger and P. Toth. Exact Solutions on the Quadratic Knapsack Problem. Informs Journal on Computing, 11(2):125--137, 1999.
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