43443657
A note on visibility graphs
Abstract Given a set S = {s1, s2,…, sn} of vertical line segments, s1, sj see each other if there is a horizontal line segment which intersects them, but does not intersect any other line segment between them. A visibility graph G of vertices {v1, v2,…, vn} is put into a one-to-one correspondence with S, such that si corresponds to v1, and edge {vi, vj} exists in G iff si, sj see each other. We prove that any visibility graph G is ipo-triangular, that is, it can be transformed into a planar multigraph with all triangular finite faces, by successive duplications of existing edges of G. Conversely we prove that any ipo-triangular graph is a visibility graph for some set S.
6074974
Vertex Ranking of Asteroidal Triple-Free Graphs
We present an efficient algorithm for computing the vertex ranking number of an asteroidal triple-free graph. Its running time is bounded by a polynomial in the number of vertices and the number of minimal separators of the input graph.
21236849
Near-Optimal Solutions to a 2-Dimensional Placement Problem
We consider the problem of placing records in a 2-dimensional storage array so that expected distance between consecutive references is minimized. A simple placement heuristic which uses only relative frequency of access for different records is shown to be within an additive constant of optimal when distance is measured by the Euclidean metric. For the rectilinear and maximum metrics, we show that there is no such heuristic. For the special case in which all access probabilities are equal, however, heuristics within an additive constant of optimal do exist, and their implementation requires solution of differential equations for which we give numerical solutions.
1566543
Minimizing Mean Flow Time with Error Constraint
Abstract. We consider the problem of minimizing mean flow time for the Imprecise Computation Model introduced by Lin et al. A task system TS=({Ti},{r(Ti)},{d(Ti)},{m(Ti)},{o(Ti)})  consists of a set of n  independent tasks, where r(Ti),d(Ti),m(Ti) , and o(Ti)  denote the ready time, deadline, execution time of the mandatory part, and execution time of the optional part of Ti , respectively. Given a task system TS  and an error threshold K , our goal is to find a preemptive schedule on one processor such that the average error is no more than K  and the mean flow time of the schedule is minimized. Such a schedule is called an optimal schedule. In this article we show that the problem of finding an optimal schedule is NP-hard, even if all tasks have identical ready times and deadlines. A pseudopolynomial-time algorithm is given for a set of tasks with identical ready times and deadlines, and oppositely ordered mandatory execution times and total execution times (i.e., there is a labeling of tasks such that m(Ti)≤ m(Ti+1)  and m(Ti)+o(Ti)≥ m(Ti+1)+o(Ti+1)  for each 1≤ i<n  ). Finally, polynomial-time algorithms are given for (1) a set of tasks with identical ready times, and similarly ordered mandatory execution times and total execution times and (2) a set of tasks with similarly ordered ready times, deadlines, mandatory execution times, and total execution times.
654791
An image signature for any kind of image
We describe an algorithm for computing an image signature, suitable for first-stage screening for duplicate images. Our signature relies on the relative brightness of image regions, and is generally applicable to photographs, text documents, and line art. We give experimental results on the sensitivity and robustness of signatures for actual image collections, and also results on the robustness of signatures under transformations such as resizing, rescanning, and compression.
26809229
Packing Squares into a Square
Abstract The problem of determining whether a set of rectangles can be orthogonally packed into a larger rectangle has been studied as a geometric packing problem and as a floor planning problem. Recently, there is some renewed interest in this problem, as it is related to a job scheduling problem in a partitionable mesh connected system. In this paper we show that the problem of deciding whether a set of squares can be packed into a larger square is strongly NP-complete, answering an open question posed by Li and Cheng.
12009161
Dynamic Placement of Records in Linear Storage
This paper considers allocation of space in a hnear storage medium when space must be allocated dynamically as customers arrive A heuristic is proposed for this problem and for a simple model of the resultmg reference sequence, we show that the average distance between consecutive references is asymptotically 7n/30, where n is the size of the storage For optimal static placement where one waits for all arrivals before any space allocation, the average distance is shown to be asymptotically 7n/30 For random placement, the average distance is asymptotically n/3 Thus, the heuristic is asymptotically optimal in a strong sense For reasonable values of n, we demonstrate that the heuristic is nearly as good as optimal static placement and much better than random placement