In this paper, we study a variant of the social network maximum influence problem and its application to intelligently approaching individual gang members with incentives to leave a gang. The goal is to identify individuals who when influenced to leave gangs will propagate this action. We study this emerging application by exploring specific facets of the problem that must be addressed when modeling this particular situation. We formulate a new influence maximization variant - the "social incentive influence" (SII) problem and study it both formally and in the context of the law-enforcement domain. Using new techniques from unconstrained submodular maximization, we develop an approximation algorithm for SII and present a suite of experimental results - including tests on real-world police data from Chicago.

Article Two Steiner tree packing problems Share on Author: William R. Pulleyblank Mathematical Sciences Department, I.B.M. Research, Yorktown Heights, NY Mathematical Sciences Department, I.B.M. Research, Yorktown Heights, NYView Profile Authors Info & Claims STOC '95: Proceedings of the twenty-seventh annual ACM symposium on Theory of computingMay 1995 Pages 383–387https://doi.org/10.1145/225058.225163Online:29 May 1995Publication History 7citation443DownloadsMetricsTotal Citations7Total Downloads443Last 12 Months4Last 6 weeks1 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteGet Access

We are given a set of points p1;...;pn and a symmetric distance matrix (dij) givingthedistancebetweenpiandpj. Wewishtoconstruct atourthatminimizesPni=1`(i),where`(i)is thelatencyofpi,denedtobethedistance traveledbeforerstvisitingpi.Thisproblem isalsoknownintheliteratureasthedeliveryman problem orthetravelingrepairmanproblem. It arises in a number ofapplicationsincluding disk-head scheduling, and turnsouttobesurprisinglydierentfromthetravelingsalesman problem in character. We give exact and approximate solutions to a number of cases, including a constant-factor approximation algorithm whenever the distance matrix satisfies the triangle inequality.

We discuss problems of optimizing the area of a simple polygon for a given set of vertices P and show that these problems are very closely related to problems of optimizing the number of points from a set Q in a simple polygon with vertex set P. We prove that it is NP-complete to find a minimum weight polygon or a maximum weight polygon for a given vertex set, resulting in a proof of NP-completeness for the corresponding area optimization problems. We show that we can find a polygon of more than half the area AR(conv(P)) of the convex hull conv(P) of P, and demonstrate that it is NP-complete to decide whether there is a simple polygon of at least (3/2 + ε)AR(conv(P)). Finally, we prove that for 1 ≤ k ≤ d, 2 ≤ d, it is NP-hard to minimize the volume of the k-dimensional faces of a d-dimensional simple non-degenerate polyhedron with a given vertex set, answering a generalization of a question stated by O'Rourke in 1980.

This paper analyzes decomposition properties of a graph that, when they occur, permit a polynomial solution of the traveling salesman problem and a description of the traveling salesman polytope by a system of linear equalities and inequalities. The central notion is that of a 3-edge cutset, namely, a set of 3 edges that, when removed, disconnects the graph. Conversely, our approach can be used to construct classes of graphs for which there exists a polynomial algorithm for the traveling salesman problem. The approach is illustrated on two examples, Halin graphs and prismatic graphs.

Abstract We consider Steiner tree problems and connected dominating set problems for several classes of graphs. We give a polynomial algorithm and a min‐max theorem for the cardinality Steiner problem in strongly chordal graphs and a polynomial algorithm for the weighted connected dominating set problem in series‐parallel graphs. We establish simple direct transformations between Steiner problems and connected domination problems for several classes of graphs and establish related NP‐completeness results.

Abstract The following type of problem arises in practice: in a node‐weighted graph G, find a minimum‐weight node set that satisfies certain conditions and, in addition, induces a perfectly matchable subgraph of G. This has led us to study the convex hull of incidence vectors of node sets that induce perfectly matchable subgraphs of a graph G, which we call the perfectly matchable subgraph polytope of G. For the case when G is bipartite, we give a linear characterization of this polytope, i.e., specify a system of linear inequalities whose basic solutions are the incidence vectors of perfectly matchable node sets of G. We derive this result by three different approaches, using linear programming duality, projection, and lattice polyhedra, respectively. The projection approach is used here for the first time as a proof method in polyhedral combinatorics, and seems to have many similar applications. Finally, we completely characterize the facets of our polytope; i.e., we separate the essential inequalities of our linear defining system from the redundant ones.