On minimum walks in graphs

In this paper homomorphisms are used to define four new parameters of a graph, which have to do with minimum walks in graphs satisfying certain conditions. Several bounds and exact equations are obtained for two of these parameters; a third parameter is seen to be closely related to the Traveling Salesman Problem and the question of whether a given graph is Hamiltonian.     

The equivalence of general set-covering and implicit integer programming formulations for shift scheduling

In a recent article we demonstrated that implicit optimal modeling for shift scheduling (P2) has inherent size and execution time advantages over the general set-covering formulation for shift scheduling (P1) [11, 13]. We postulated that the absence of extraordinary overlap (EO) was a requirement for the equivalence of P1 and P2. We have defined EO as the condition in which the earliest and latest starts for a break in one shift are earlier and later than the earliest and latest starts for a break in any other shift(s). In this article, we prove that our earlier postulate was accurate. Additionally, we discuss research extensions and note other scheduling problems for which implicit modeling may be appropriate. © 1996 John Wiley & Sons, Inc.     

How Is a Man to Decide? Unjust Combatants,Duress and McMahan’s Killing in War

Jeff McMahan’s much-discussed work Killing in War is an important part of the revisionist school of just war studies. This paper avoids discussion of McMahan’s use of human rights and examines the practical consequences of his argument about duress on soldiers to fight an unjust war. These arguments are found to be wanting and to be impractical ones that do not fit battlefield realities. The importance of the Law of Armed Conflict and the legal equality of combatants that is part of it is emphasised and accepted as the most practical way of regulating battlefield behaviour and saving lives. It is concluded that attempts to tell soldiers what to do when they may be fighting an unjust war add to their burdens and are misplaced.     

Beyond the Double Game: Lessons from Pakistan’s Approach to Islamist Militancy

States commonly take one of three approaches to militant groups on their soil: collaboration; benign neglect; or belligerence. All three approaches are present in Pakistan, where some groups also move back and forth among these categories. I employ the term “coopetition” to capture this fluidity. The dynamic nature of militancy in Pakistan makes the country an excellent laboratory for exploring a state’s assessment of the utility an Islamist militant group offers, and the threat it poses relative to other threats informs the state’s treatment of that group. In this article, I put forward a typology that situates Islamist militants in Pakistan in one of the above four categories. I also illustrate how a group’s identity, objectives, and alliances inform assessments of its utility and threat relative to other threats. In addition to enhancing our understanding of militant–state dynamics, this taxonomy builds on and helps to unify earlier typologies of Pakistani militancy.