Subset sum problems with digraph constraints

We introduce and study optimization problems which are related to the well-known Subset Sum problem. In each new problem, a node-weighted digraph is given and one has to select a subset of vertices whose total weight does not exceed a given budget. Some additional constraints called digraph constraints and maximality need to be satisfied. The digraph constraint imposes that a node must belong to the solution if at least one of its predecessors is in the solution. An alternative of this constraint says that a node must belong to the solution if all its predecessors are in the solution. The maximality constraint ensures that no superset of a feasible solution is also feasible. The combination of these constraints provides four problems. We study their complexity and present some approximation results according to the type of input digraph, such as directed acyclic graphs and oriented trees

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

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