Abstract-Regression testing is a necessary but expensive maintenance activity aimed at showing that code has not been adversely affected by changes. Regression test selection techniques reuse tests from an existing test suite to test a modified program. Many regression test selection techniques have been proposed; however, it is difficult to compare and evaluate these techniques because they have different goals. This paper outlines the issues relevant to regression test selection techniques, and uses these issues as the basis for a framework within which to evaluate the techniques. We illustrate the application of our framework by using it to evaluate existing regression test selection techniques. The evaluation reveals the strengths and weaknesses of existing techniques, and highlights some problems that future work in this area should address. Index Terms-Software maintenance, regression testing, selective retest, regression test selection. 1

The Davis-Putnam enumeration method (DP) has recently become one of the fastest known methods for solving the clausal satisfiability problem of propositional calculus. We present a generalization of the DP-procedure for solving the satisfiability problem of a set of linear pseudo-Boolean (or 0-1) inequalities. We extend the method to solve linear 0-1 optimization problems, i.e. optimize a linear pseudo-Boolean objective function w.r.t. a set of linear pseudo-Boolean inequalities. The algorithm compares well with traditional linear programming based methods on a variety of standard 0-1 integer programming benchmarks. Keywords 0-1 Integer Programming; Propositional Calculus; Enumeration Contents 1 Introduction 1 2 Preliminaries 1 3 The Classical Davis-Putnam Procedure 3 4 Davis-Putnam for Linear Pseudo-Boolean Inequalities 5 5 Optimizing with Pseudo-Boolean Davis-Putnam 7 6 Implementation 8 7 Heuristics 10 8 Computational Results 10 9 Conclusion 12 1 Introduction The Davis-Putn...

In this paper, we investigate the use of Gomory's mixed integer cuts within a branch-and-cut framework. It has been argued in the literature that "a marriage of classical cutting planes and tree search is out of the question as far as the solution of large-scale combinatorial optimization problems is concerned" [16] because the cuts generated at one node of the search tree need not be valid at other nodes. We show in this paper that it is possible, using a simple lifting procedure, to make Gomory cuts generated in a node of the enumeration tree globally valid in the case of mixed 0-1 programs. Other issues addressed in this paper are of computational nature, such as strategies for generating the cutting planes, deciding between branching and cutting, etc. The result is a robust mixed integer program solver. 1 Introduction In the late fifties and early sixties, Gomory [6], [7], [8] proposed to solve integer programs by using cutting planes, thus reducing integer programming to the solu...

this paper, now include cutting-plane capabilities as well as other ideas from the backlog of accumulated theory. As suggested by the title of this paper, the gap between theory and practice is indeed closing

Dantzig, Fulkerson, and Johnson (1954) introduced the cutting-plane method as a means of attacking the traveling salesman problem; this method has been applied to broad classes of problems in combinatorial optimization and integer programming. In this paper we discuss an implementation of Dantzig et al.'s method that is suitable for TSP instances having 1,000,000 or more cities. Our aim is to use the study of the TSP as a step towards understanding the applicability and limits of the general cutting-plane method in large-scale applications.

The network loading problem (NLP) is a specialized capacitated network design problem in which prescribed point-to-point demand between various pairs of nodes of a network must be met by installing (loading) a capacitated facility. We can load any number of units of the facility on each of the arcs at a specified arc dependent cost. The problem is to determine the number of facilities to be loaded on the arcs that will satisfy the given demand at minimum cost. This paper studies two core subproblems of the NLP. The first problem, motivated by a Lagrangian relaxation approach for solving the problem, considers a multiple commodity, single arc capacitated network design problem. The second problem is a three node network; this specialized network arises in larger networks if we aggregate nodes. In both cases, we develop families of facets and completely characterize the convex hull of feasible solutions to the integer programming formulation of the problems. These results in turn strengthen the formulation of the NLP.

The design of cost-efficient networks satisfying certain survivability

We describe a new convex quadratic programming bound for the quadratic assignment problem (QAP). The construction of the bound uses a semidefinite programming representation of a basic eigenvalue bound for QAP. The new bound dominates the well-known projected eigenvalue bound, and appears to be competitive with existing bounds in the tradeoff between bound quality and computational effort. Keywords: Quadratic Assignment Problem, Eigenvalue Bounds, Quadratic Programming, Semidefinite Programming. Dept. of Management Sciences, University of Iowa, Iowa City, IA 52242 y Dept. of Computer Science, University of Iowa, Iowa City, IA 52242 1 Introduction The quadratic assignment problem (QAP) in "Koopmans-Beckmann" form can be written QAP(A;B;C) : min tr(AXB + C)X T s:t: X 2 \Pi; where A, B and C are n \Theta n matrices, tr denotes the trace of a matrix, and \Pi is the set of n \Theta n permutation matrices. Throughout we assume that A and B are symmetric. The QAP is a very well-know...

Knapsack constraints are a key modeling structure in constraint programming. These constraints are normally handled with simple bounding arguments. We propose a dynamic programming structure to represent these constraints. With this structure, we show how to achieve hyper-arc consistency, to determine infeasibility before all variables are set, to generate all solutions quickly, and to update the structure after domain reduction. Preliminary testing on a dicult set of multiple knapsack instances shows signicant reduction in branching, though an eective implementation is needed in order to reduce computation time. Keywords: Global Constraints, Dynamic Programming, Knapsack Constraints 1.

Branch-and-cut methods are very successful techniques for solving a wide variety of integer programming problems, and they can provide a guarantee of optimality. We describe how a branch-and-cut method can be tailored to a specific integer programming problem, and how families of general cutting planes can be used to solve a wide variety of problems. Other important aspects of successful implementations are discussed in this chapter. The area of branch-and-cut algorithms is constantly evolving, and it promises to become even more important with the exploitation of faster computers and parallel computing. 1