A plane graph representation of triconnected graphs

AbstractGiven a graph G=(V,E), a set S={s1,s2,…,sk} of k vertices of V, and k natural numbers n1,n2,…,nk such that ∑i=1kni=|V|, the k-partition problem is to find a partition V1,V2,…,Vk of the vertex set V such that |Vi|=ni, si∈Vi, and Vi induces a connected subgraph of G for each i=1,2,…,k. For the tripartition problem on a triconnected graph, a naive algorithm can be designed based on a directional embedding of G in the two-dimensional Euclidean space. However, for graphs of large number of vertices, the implementing of this algorithm requires high precision real arithmetic to distinguish two close vertices in the plane. In this paper, we propose an algorithm for dealing with the tripartition problem by introducing a new data structure called the region graph, which represents a kind of combinatorial embedding of the given graph in the plane. The algorithm constructs a desired tripartition combinatorially in the sense that it does not require any geometrical computation with actual coordinates in the Euclidean space

Balancing Graph Voronoi Diagrams

Abstract—Many facility location problems are concerned with minimizing operation and transportation costs by par-titioning territory into regions of similar size, each of which is served by a facility. For many optimization problems, the overall cost can be reduced by means of a partitioning into balanced subsets, especially in those cases where the cost associated with a subset is superlinear in its size. In this paper, we consider the problem of generating a Voronoi partition of a discrete graph so as to achieve balance conditions on the region sizes. Through experimentation, we first establish that the region sizes of randomly-generated graph Voronoi diagrams vary greatly in practice. We then show how to achieve a balanced partition of a graph via Voronoi site resampling. For bounded-degree graphs, where each of the n nodes has degree at most d, and for an initial randomly-chosen set of s Voronoi nodes, we prove that, by extending the set of Voronoi nodes using an algorithm by Thorup and Zwick, each Voronoi region has size at most 4dn/s+1 nodes, and that the expected size of the extended set of Voronoi nodes is at most 2s logn. Keywords-graph Voronoi diagram; balancing; facility loca-tion; territorial design I

Developing techniques for enhancing comprehensibility of controlled medical terminologies

A controlled medical terminology (CMT) is a collection of concepts (or terms) that are used in the medical domain. Typically, a CMT also contains attributes of those concepts and/or relationships between those concepts. Electronic CMTs are extremely useful and important for communication between and integration of independent information systems in healthcare, because data in this area is highly fragmented. A single query in this area might involve several databases, e.g., a clinical database, a pharmacy database, a radiology database, and a lab test database. Unfortunately, the extensive sizes of CMTs, often containing tens of thousands of concepts and hundreds of thousands of relationships between pairs of those concepts, impose steep learning curves for new users of such CMTs. In this dissertation, we address the problem of helping a user to orient himself in an existing large CMT. In order to help a user comprehend a large, complex CMT, we need to provide abstract views of the CMT. However, at this time, no tools exist for providing a user with such abstract views. One reason for the lack of tools is the absence of a good theory on how to partition an overwhelming CMT into manageable pieces. In this dissertation, we try to overcome the described problem by using a threepronged approach. (1) We use the power of Object-Oriented Databases to design a schema extraction process for large, complex CMTs. The schema resulting from this process provides an excellent, compact representation of the CMT. (2) We develop a theory and a methodology for partitioning a large OODI3 schema, modeled as a graph, into small meaningful units. The methodology relies on the interaction between a human and a computer, making optimal use of the human\u27s semantic knowledge and the computer\u27s speed. Furthermore, the theory and methodology developed for the scbemalevel partitioning are also adapted to the object-level of a CMT. (3) We use purely structural similarities for partitioning CMTs, eliminating the need for a human expert in the partitioning methodology mentioned above. Two large medical terminologies are used as our test beds, the Medical Entities Dictionary (MED) and the Unified Medical Language System (UMLS), which itself contains a number of terminologies

Most uniform path partitioning and its use in image processing

SIGLEAvailable from Bibliothek des Instituts fuer Weltwirtschaft, ZBW, Duesternbrook Weg 120, D-24105 Kiel / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

An algorithmic approach to continuous location

Bibliography: pages 126-130.We survey the p-median problem and the p-centre problem. Then we investigate two new techniques for continuous optimal partitioning of a tree T with n - 1 edges, where a nonnegative rational valued weight is associated with each edge. The continuous Max-Min tree partition problem (the continuous Min-Max tree partition problem) is to cut the edges in p - 1 places, so as to maximize (respectively minimize) the weight of the lightest (respectively heaviest) resulting subtree. Thus the tree is partitioned into approximately equal components. For each optimization problem, an inefficient implementation of the algorithm is given, which runs in pseudo-polynomial time, using a previously developed algorithm and a construction. We then derive from it a much faster algorithm using a top-down greedy technique, which runs in polynomial time. The algorithms have a variety of applications among others to highway and pipeline maintenance