16381803
Upper and lower bounds for graph-diameter problems with application to record allocation
This paper studies three graph problems with parameters n, the number of nodes, e, the number of edges, and k, the diameter of the graph. Given any two of these three parameters, the problem is to construct a directed graph which minimizes or maximizes the third. The first problem has its origin in a recent study of record allocation in a paged computer system. It is shown how to construct graphs that are optimal for all three problems in some cases and are asymptotically optimal for other cases. The solution of the second problem answers a question raised by Berge in “The Theory of Graphs and its Application,” 1962.
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.
34486647
Minimum Fill-In on Circle and Circular-Arc Graphs
We present two algorithms solving the minimum fill-in problem on circle graphs and on circular-arc graphs in time O(n3).
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.
195859283
On fixed edges and edge-reconstruction of series-parallel networks
A graph configuration is a vertex labeled simple graph. We say a configuration is exclusive for graphs with a property in a class of graphs if every graph in the class containing the configuration has the property. We use the method of exclusive configurations to search for graphs without fixed edges and forced edges investigate the fixed edges. An edge e of a graph G is said to be a fixed edge if G-e+e'/spl cong/G implies that e'=e, and a forced edge if G-e+e' is an edge-reconstruction of G implies that e'=e. It is proved that all series-parallel networks contain fixed edges and forced edge except P/sub 2//spl times/K/sub 1/ and P/sub 3//spl times/K/sub 1/. A similar method is used to investigate the alternative wire problem in circuit design. Let G be a Boolean network and w a wire in G. Wire w' is said to be an alternative wire of w if w'/spl ne/w and G-w+w' has the same functionality as that of G. A wire is said to be fixed if it has no alternative wire. We present a set of exclusive configurations for Boolean networks in which every wire is fixed.
15615911
Time-varying shortest path problems with constraints
The shortest path problem is considered with yet another extension. The transit times b(x,y,u) and the arc costs c(x,y,u) on arc (x,y) vary as a function of the departure time u at the beginning vertex of the arc. The problem considered is to find the shortest path between a pair of nodes such that the total traverse time is lesser than some specified value T. Waiting times at nodes are considered as decision variables in this paper as well. Three variations of the problem are analyzed in which the waiting times are allowed to be arbitrary, the waiting times are zero and the waiting time has an upper bound at each vertex. Algorithms are also discussed to solve the problem. Some of the applications of the problem are encountered in communication networks and freight delivery problems. Suppose that some freight is to be sent from one city to another in a network before a deadline T. Different types of freight services with different costs and transit times are available between the two cities. An optimal solution would have to specify the route as well as the waiting times of the freight at each city so that the overall cost is minimum. A dynamic programming approach is used to compute the shortest path from the origin node to the destination node. Three cases are considered for the waiting times and an algorithm is suggested for each of those cases. This problem is obviously an NP-Complete problem as it is more difficult to solve than a problem with constant transit times and arc costs such as the previous problem which is NP-Complete. Some definitions: Waiting time w(x i) at a vertex x i is a nonnegative integer with an upper bound U x >= 0. Let P be a path from vertex x 1 to x r. The departure time T(x i) at a vertex x i can be expressed as below: T(x 1) = w(x 1) The departure time for all other vertices on the path can be expressed recursively as : The time of path P is defined as T(x r) where x r is the final node on the path..
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
14489674
Automatic lyrics alignment for Cantonese popular music
From lyrics-display on electronic music players and Karaoke videos to surtitles for live Chinese opera performance, one feature is common to all these everyday functionalities temporal: synchronization of the written text and its corresponding musical phrase. Our goal is to automate the process of lyrics alignment, a procedure which, to date, is still handled manually in the Cantonese popular song (Cantopop) industry. In our system, a vocal signal enhancement algorithm is developed to extract vocal signals from a CD recording in order to detect the onsets of the syllables sung and to determine the corresponding pitches. The proposed system is specifically designed for Cantonese, in which the contour of the musical melody and the tonal contour of the lyrics must match perfectly. With this prerequisite, we use a dynamic time warping algorithm to align the lyrics. The robustness of this approach is supported by experiment results. The system was evaluated with 70 twenty-second music segments and most samples have their lyrics aligned correctly.
7180182
Minimizing mean flow time with error constraint
In a new model of task systems studied by J.W.S. Liu et al. (1987) each task is logically decomposed into two subtasks, mandatory and optional. The authors discuss preemptively scheduling this kind of task system on p>or=1 identical processors so as to minimize the mean flow time. Given a task system and an error threshold K, the goal is to find a preemptive schedule such that each task is executed in the interval of its release time and deadline, 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. It is shown that the problem of finding an optimal schedule is NP-hard for each p>or=1, even if all tasks have the same ready time and deadline. For a single processor, a pseudo-polynomial time algorithm and polynomial time algorithms for various special cases of the problem are given.<<ETX>>
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.
31592050
Analysis of a General Mass Storage System
A model of a general mass storage system is presented and its performance analyzed. The system is composed of a square two-dimensional grid of storage cells over which a single read/write head moves freely. The head can contain at most some fixed number b of cell contents. Algorithms for realizing an arbitrary permutation of the memory contents are presented for all ranges of b, particularly the important case $b = 1$; in each case the algorithms’ performances are explicitly characterized. Open problems, especially regarding the development of good heuristics, are then discussed.