A generalization of the weighted set covering problem

We study a generalization of the weighted set covering problem where every element needs to be covered multiple times. When no set contains more than two elements, we can solve the problem in polynomial time by solving a corresponding weighted perfect b‐matching problem. In general, we may use a polynomial‐time greedy heuristic similar to the one for the classical weighted set covering problem studied by D.S. Johnson [Approximation algorithms for combinatorial problems, J Comput Syst Sci 9 (1974), 256–278], L. Lovasz [On the ratio of optimal integral and fractional covers, Discrete Math 13 (1975), 383–390], and V. Chvatal [A greedy heuristic for the set‐covering problem, Math Oper Res 4(3) (1979), 233–235] to get an approximate solution for the problem. We find a worst‐case bound for the heuristic similar to that for the classical problem. In addition, we introduce a general type of probability distribution for the population of the problem instances and prove that the greedy heuristic is asymptotically optimal for instances drawn from such a distribution. We also conduct computational studies to compare solutions resulting from running the heuristic and from running the commercial integer programming solver CPLEX on problem instances drawn from a more specific type of distribution. The results clearly exemplify benefits of using the greedy heuristic when problem instances are large. © 2003 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

Book reviews

Frank Zimmer, Bismarcks Kampf gegen Kaiser Franz Joseph Konigsgratz und seine Folgen. Graz, Vienna, Cologne: Styria Verlag 1996. Pp.203,49 illus., 1 map. OS 350/DM 49. ISBN 3–222–12377–2.

Saul Zadka, Blood in Zion: How the Jewish Guerrillas drove the British out of Palestine. London and Washington: Brassey's, 1995. Pp.227, chron., illus., index. £19.95. ISBN 1–85753–136–1.

Theodore L. Gatchel, At the Water's Edge: Defending against the Modern Amphibious Assault. Annapolis, MD: Naval Institute Press, 1996. Pp.xvi+217, notes, biblio, index. $36.95. ISBN 1–55750–308–7.

Max G. Manwaring and William J. Olson (eds.) Managing Contemporary Conflict: Pillars of Success. Boulder, CO: Westview Press, 1996. Pp.269, no index. $65 (cloth); $25 (paper). ISBN 0–8133–8969 and 9978–5

Chris Seiple, The US Military/NGO Relationship in Humanitarian Interventions, Carlisle Barracks, PA: The

Richard L. Millett and Michael Gold‐Biss (eds.) Beyond Praetorianism: The Latin American Military in Transition. University of Miami: North/South Center Press; Boulder, CO: Lynne Rienner, 1996. Pp.xv +317, index. $24.95. ISBN 1–5745–000–9.

Rudolph C. Barnes Jr, Military Legitimacy: Might and Right in the New Millennium. London and Portland, OR: Frank Cass, 1996. Pp.199, select biblio., index. £27.50/$39.50, ISBN 0–714–4624–5.     

Defense spending and economic growth across the Taiwan straits: a threshold regression model

This paper employs both linear and non‐linear models to investigate the relationship between national defense spending and economic growth for Taiwan and China. Using data from 1953–2000 on defense spending, GDP, import, export and capital, we find that China's defense spending leads that of Taiwan. There exists the phenomenon of an arms race between both countries when official Chinese data are used. On the one hand, feedback relations prevail between economic growth and defense spending growth in Taiwan. On the other hand, China's national defense is found to lead economic growth.     

THE FATE OF DISPUTED TERRITORIES: AN ECONOMIC ANALYSIS

This paper presents a simple model to characterize the outcome of a land dispute between two rival parties using a Stackelberg game. Unlike Gershenson and Grossman (2000 Gershenson, D. and Grossman, H.I. 2000. Civil conflict: ended or never ending?. Journal of Conflict Resolution, 44(6): 807–821.  [Google Scholar]), we assume that the opposing parties have access to different technologies for challenging and defending in conflict. We derive the conditions under which territorial conflict between the two parties is less likely to persist indefinitely. Allowing for an exogenous destruction term as in Garfinkel and Skaperdas (2000 Garfinkel, M. and Skaperdas, S. 2000. Conflict without misperceptions or incomplete information: how the future matters. Journal of Conflict Resolution, 44(6): 793–807. [Crossref], [Web of Science ®] , [Google Scholar]), we show that, when the nature of conflict becomes more destructive, the likelihood of a peaceful outcome, in which the territory’s initial possessor deters the challenging party, increases if the initial possessor holds more intrinsic value for the disputed land. Following Siqueira (2003 Siqueira, K. 2003. Conflict and third‐party intervention. Defence and Peace Economics, 14(6): 389–400. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]), our model has policy implications for peace through third‐party intervention.     

A PANEL DATA ANALYSIS OF THE NEXUS BETWEEN DEFENCE SPENDING AND GROWTH IN THE EUROPEAN UNION: A REPLY

Hatzinikolaou raises a number of issues related mainly to the econometrics of our paper. These issues are categorized according to the three stages of econometric analysis: specification, estimation, and diagnostic checking. We categorize our reply to his comments accordingly.