58 research outputs found
Good Fences: The Importance of Setting Boundaries for Peaceful Coexistence
We consider the conditions of peace and violence among ethnic groups, testing
a theory designed to predict the locations of violence and interventions that
can promote peace. Characterizing the model's success in predicting peace
requires examples where peace prevails despite diversity. Switzerland is
recognized as a country of peace, stability and prosperity. This is surprising
because of its linguistic and religious diversity that in other parts of the
world lead to conflict and violence. Here we analyze how peaceful stability is
maintained. Our analysis shows that peace does not depend on integrated
coexistence, but rather on well defined topographical and political boundaries
separating groups. Mountains and lakes are an important part of the boundaries
between sharply defined linguistic areas. Political canton and circle
(sub-canton) boundaries often separate religious groups. Where such boundaries
do not appear to be sufficient, we find that specific aspects of the population
distribution either guarantee sufficient separation or sufficient mixing to
inhibit intergroup violence according to the quantitative theory of conflict.
In exactly one region, a porous mountain range does not adequately separate
linguistic groups and violent conflict has led to the recent creation of the
canton of Jura. Our analysis supports the hypothesis that violence between
groups can be inhibited by physical and political boundaries. A similar
analysis of the area of the former Yugoslavia shows that during widespread
ethnic violence existing political boundaries did not coincide with the
boundaries of distinct groups, but peace prevailed in specific areas where they
did coincide. The success of peace in Switzerland may serve as a model to
resolve conflict in other ethnically diverse countries and regions of the
world.Comment: paper pages 1-14, 4 figures; appendices pages 15-43, 20 figure
New bounds on optimal BSTs trees
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2006.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Includes bibliographical references (p. 153-156).Binary search trees (BSTs) are a class of simple data structures used to store and access keys from an ordered set. They have been around for about half a century. Despite their ubiquitous use in practical programs, surprisingly little is known about their optimal performance. No polynomial time algorithm is known to compute the best BST for a given sequence of key accesses, and before our work, no o(log n)-competitive online BST data structures were known to exist. In this thesis, we describe tango trees, a novel O(log log n)-competitive BST algorithm. We also describe a new geometric problem equivalent to computing optimal offline BSTs that gives a number of interesting results. A greedy algorithm for the geometric problem is shown to be equivalent to an offline BST algorithm posed by Munro in 2000. We give evidence that suggests Munro's algorithm is dynamically optimal, and strongly suggests it can be made online. The geometric model also lets us prove that a linear access algorithm described by Munro in 2000 is optimal within a constant factor. Finally, we use the geometric model to describe a new class of lower bounds that includes both of the major earlier lower bounds for the performance of offline BSTs, and construct an optimal bound in this new class.by Dion Harmon.Ph.D
Dynamic Optimality–Almost
We present an O(lg lg n)-competitive online binary search tree, improving upon the best previous (trivial) competitive ratio of O(lg n). This is the first major progress on Sleator and Tarjan’s dynamic optimality conjecture of 1985 that O(1)-competitive binary search trees exist. 1
Dynamic Optimality–Almost
We present an O(lg lg n)-competitive online binary search tree, improving upon the best previous (trivial) competitive ratio of O(lg n). This is the first major progress on Sleator and Tarjan’s dynamic optimality conjecture of 1985 that O(1)-competitive binary search trees exist.
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