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A set, V, of points in the plane is triangulated by a subset T, of the straight-line segments whose endpoints are in V, if T is a maximal subset such that the line segments in T intersect only at their endpoints. The weight of any triangulation is the sum of the Euclidean lengths of the line segments in the triangulation. We examine two problems involving triangulations. We discuss the problem of...
Fully polynomial approximation algorithms for knapsack problems are presented. These algorithms are based on ideas of Ibarra and Kim, with modifications which yield better time and space bounds, and also tend to improve the practicality of the procedures. Among the principal improvements are the introduction of a more efficient method of scaling and the use of a median-finding routine to eliminate...
A combinatorial problem related to storage allocation is analyzed. The problem falls into a class of NP-complete, one-dimensional bin-packing problems. We propose an iterative approximation algorithm and show that it is superior to an earlier heuristic presented for this problem. The bulk of the paper is devoted to the proof of a worst-case performance bound.
We argue that relative soundness and completeness theorems for Floyd-Hoare Axiom Systems ([6], [5], [18]) are really fixed point theorems. We give a characterization of program invariants as fixed points of functionals which may be obtained in a natural manner from the text of a program. We show that within the framework of this fixed point theory, relative soundness and completeness results have...
A number of decision problems that are unsolvable in general are solvable when restricted to systems with sufficiently simple "loop structure". Examples of such problems are the equivalence problems for flowchart schemata with nonintersecting loops and for the LOOP(l) programs of Meyer and Ritchie. We here present a theorem that gives a unifying view of the solvability of both of these problems,...
This paper gives new results, and presents old ones in a unified formalism, concerning Church-Rosser theorems for rewriting systems. Part 1 gives abstract confluence properties, depending solely on axioms for a binary relation called reduction. Results of Newman and others are presented in a unified formalism. Systematic use of a powerful induction principle permits to generalize results of Sethi...
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