Combinatorial optimization is a lively eld of applied mathematics, combining techniques from combinatorics, linear programming, and the theory of algorithms, to solve optimization problems over discrete structures. There are a number of classic texts in this eld, but we felt that there is a place for a new treatment of the subject, covering some of the advances that have been made in the past decade. We set out to describe the material in an elementary text, suitable for a one semester course. The urge to include advanced topics proved to be irresistible, however, and the manuscript, in time, grew beyond the bounds of what one could reasonably expect to cover in a single course. We hope that this is a plus for the book, allowing the instructor to pick and choose among the topics that are treated. In this way, the book may b e s u i table for both graduate and undergraduate courses, given in departments of mathematics, operations research, and computer science. An advanced theoretical course might spend a lecture or two o n c hapter 2 and sections 3.1 and 3.2, then concentrate on 3.3, 3.4, 4.1, most of chapters 5 and 6 and some of chapters 8 and 9. An introductory course might c o ver chapter 2, sections 3.1 to 3.3, section 4.1 and one of 4.2 or 4.3, and sections 5.1 through 5.3. A course oriented more towards integer linear programming and polyhedral methods could be based mainly on chapters 6 and 7 and would include section 3.6. The most challenging exercises have been marked in boldface. These should probably only be used in advanced courses. The only real prerequisite for reading our text is a certain mathematical maturity. W e d o m a k e frequent use of linear programming duality, so a reader unfamiliar with this subject matter should be prepared to study the linear programming appendix before proceeding with the main part of the text. We bene tted greatly from thoughtful comments given by m a n y o f o u r colleagues who read early drafts of the book. In particular, we w ould like to thank

Who are the socially conscious consumers? This article typologically classifies socially conscious consumers and evaluates the relative sensitivity of demographic and sociopsychological variables in discriminating degree of social consciousness.

Given a finite undirected graphGandA⊆E(G),G(A)denotes the subgraph ofGhaving edge-setAand having no isolated vertices. For a partition {E1, E2}ofE(G),W(G; E1)denotes the setV(G(E1))⋂V(G(E2)). We say thatGisnon-separableif it is connected and for every proper, non-empty subsetAofE(G), we have |W(G;A)| ≧ 2. Asplitof a non-separable graphGis a partition {E1, E2} ofE(G)such that|E1| ≧ 2 ≧ |E2| and |W(G; E1)| = 2.Where {E1, E2} is a split ofG, W(G; E2)= {u, v}, andeis an element not inE(G),we form graphsGii= 1 and 2, by addingetoG(Ei)as an edge joiningutov.

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In a nonnegative edge-weighted network, the weight of an edge represents the effort required by an attacker to destroy the edge, and the attacker derives a benefit for each new component created by destroying edges. The attacker may want to minimize over subsets of edges the difference between (or the ratio of) the effort incurred and the benefit received. This idea leads to the definition of the “strength” of the network, a measure of the resistance of the network to such attacks. Efficient algorithms for the optimal attack problem, the problem of computing the strength, and the problem of finding a minimum cost “reinforcement” to achieve a desired strength are given. These problems are also solved for a different model, in which the attacker wants to separate vertices from a fixed central vertex.