We show that the minimum fill-in and the minimum interval graph completion of a d-trapezoid graph can be computed in time O(n). We also show that the treewidth and the pathwidth of a d-trapezoid graph can be computed by an O(n tw(G) ) time algorithm. For both algorithms, d is supposed to be a fixed positive integer and it is required that a suitable intersection model of the given d-trapezoid g...

Abstract The purpose of this paper is to extend the TOPSIS (Technique for Order Performance by Similarity to Ideal Solution) method for solving multiple attribute decision making (MADM) problems with trapezoid fuzzy linguistic variables. To begin with, this paper introduces the concept of the trapezoid fuzzy linguistic variables, and defines the distance between two trapezoid fuzzy linguistic v...

Consider two parallel lines (denoted r1 and r2). A graph is a PI graph (Point-Interval graph) if it is an intersection graph of a family F of triangles between r1 and r2 such that each triangle has an interval with two endpoints on r1 and a vertex (a point) on r2. The family F is the PI representation of G. The PI graphs are an extension of interval and permutation graphs and they form a subcla...

An algorithm that decomposes a line image into singular and regular regions is presented. We define a contour trapezoid as the building block of regular regions, and postulate a Maximal Trapezoid Set as the core of regular regions. Then, we describe an algorithm that calculates a Maximal Trapezoid Set of a polygon and show how to use it to find a skeleton of a polygonal approximation of a conto...

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A 58-year-old female developed avascular necrosis of her trapezoid approximately 3 months after undergoing carpometacarpal arthroplasty. The patient was treated conservatively with immobilization and had complete resolution of her clinical symptoms during her year of follow-up. Additionally, radiographic examination showed complete restoration of the height of her trapezoid approximately 1 year...

Trapezoid maps are a kind of continuous and piecewise linear maps with a flat top. By the conjugacy relationship, we present a complete classification for four families of trapezoid maps. Firstly, using an extension method, we construct all homeomorphic solutions of conjugacy equation φ ◦ f = g ◦ φ for some non-monotone continuous maps f and g. Secondly, using an iterative construction method a...

This paper analyzes what structural features of graph problems allow efficient parallel algorithms. We survey some parallel algorithms for typical problems on three kinds of graphs, outerplanar graphs, trapezoid graphs and in-tournament graphs. Our results on the shortest path problem, the longest path problem and the maximum flow problem on outerplanar graphs, the minimum-weight connected domi...