Steven B. Horton

Things fall apart: the endgame dynamics of internal wars

Abstract Most internal wars end on the battlefield. Only a small percentage end at the negotiating table. While significant attention has been paid to how internal wars begin and how they evolve, relatively little attention has been paid to how they are concluded. What research has been done on this subject, furthermore, has focused almost exclusively on the problems that stand in the way of achieving a negotiated outcome, not on how these conflicts are so frequently resolved by force. This article examines the dynamics of the endgame struggle and the quite different ways in which states and insurgencies ‘win’ and ‘lose’ internal wars. We explore this topic theoretically and empirically in the first part of the article and examine the formal logic of the endgame in the second part, explaining how and why these endings follow a predictable pattern.

On domination and reinforcement numbers in trees

The reinforcement number of a graph is the smallest number of edges that have to be added to a graph to reduce the domination number. We introduce the k-reinforcement number of a graph as the smallest number of edges that have to be added to a graph to reduce the domination number by k. We present an O(k^2n) dynamic programming algorithm for computing the maximum number of vertices that can be dominated using @c(G)-k dominators for trees. A corollary of this is a linear-time algorithm for computing the k-reinforcement number of a tree. We also discuss extensions and related problems.

On minimum cuts and the linear arrangement problem

In this paper we examine the problem of finding minimum cuts in finite graphs with the side constraint that the vertex sets inducing these cuts must be of a given cardinality. As it turns out, this computation is of interest not only from a combinatorial perspective but also from a practical one, pertaining to the linear arrangement value of graphs. We look at some graph classes where these cuts can be efficiently computed (in general this computation is NP-hard) as well as some cases where their value can be determined in closed form.

The linear arrangement problem on recursively constructed graphs

The linear arrangement problem on graphs is a relatively old and quite well-known problem. Hard in general, it remains open on general recursive graphs (i.e., partial k-trees, etc.), which is somewhat frustrating since most hard graph problems are easily solved on recursive graphs. In this paper, we examine the linear arrangement problem with respect to these structures. Included are some negative (complexity) results as well as a solvable case.