Showing papers on "Adjacency list published in 1987"
TL;DR: A parallel algorithm for partitioning the vertices of a graph intop≥2 sets in such a way that few edges connect vertices in different sets is developed, based on the Kernighan-Lin algorithm for finding small edge separators on a single processor.
Abstract: We develop a parallel algorithm for partitioning the vertices of a graph into $p \geq 2$ sets in such a way that few edges connect vertices in different sets The algorithm is intended for a message-passing multiprocessor system, such as the hypercube, and is based on the Kernighan-Lin algorithm for finding small edge separators on a single processor We use this parallel partitioning algorithm to find orderings for factoring large sparse symettric positive definite matrices These orderings not only reduce fill, but also result in good processor utilization and low communication overhead during the factorization We provide a complexity analysis of the algorithm, as well as some numerical results from an Intel hypercube and a hypercube simulator
87 citations
TL;DR: This paper presents the quadcode system, which is a direct description of the image, and discusses the geometric concepts in terms of the coded images themselves.
Abstract: The quadcode is a hierarchical data structure for describing digital images It has the following properties: (1) straightforward representation of dimension, size, and the relationship between an image and its subsets; (2) explicit description of geometric properties, such as location, distance, and adjacency; and (3) ease of conversion from and to raster representation The quadcode has applications to computer graphics and image processing because of its ability to focus on selected subsets of the data and to allow utilization of multiple resolutions in different parts of the image A related approach is the quadtree Samet recently presented a thorough survey of the literature in that field [7] Gargantini [2] and Abel and Smith [1] presented linear quadtrees and linear locational keys that are efficient labeling techniques for quadtrees In those papers the geometric concepts of the image are discussed by using the tree as an interpretive medium, and the approaches and procedures are based on traversal of the nodes in the tree In this paper we present the quadcode system, which is a direct description of the image, and discuss the geometric concepts in terms of the coded images themselves
43 citations
01 Jan 1987
TL;DR: In this paper, the authors define the graph Γ(G, H, a) to be the graph on the set of left-cosets of a group G, a subgroup H and an element a ∈ G, where two left cosets g1H and g2H are adjacent whenever.
Abstract: Given a group G, a subgroup H and an element a ∈ G, we define Γ(G, H, a) to be the graph on the set of left-cosets of H in G, where two left-cosets g1H and g2H are adjacent whenever . We will consider this construction only in the case thatThe first of these conditions assures that adjacency is a symmetric relation (i.e. that Γ(G, H, a) is an undirected graph) and the second assures that Γ(G, H, a) is connected.
38 citations
TL;DR: An abstract graph module that allows for easy and secure programming of a great number of graph algorithms is implemented by symmetrically stored forward and backward adjacency lists, thus supporting edge-oriented traversals of general directed and undirected graphs.
Abstract: An abstract graph module that allows for easy and secure programming of a great number of graph algorithms is implemented by symmetrically stored forward and backward adjacency lists, thus supporting edge-oriented traversals of general directed and undirected graphs.
36 citations
TL;DR: Using an MLG to index positions and attributions of objects in computer memory permits a near neighbor algorithm to be based on a “maximum index offset”, Nc, rather than a short range “cutoff” distance Rc, thus permitting efficient vectorization of computations.
31 citations
12 Oct 1987
TL;DR: A new algorithm based on ear decomposition for testing vertex four-connectivity and for finding all separating triplets in a triconnected graph is presented, which improves previous bounds for the problem for both the sequential and parallel cases.
Abstract: We present a new algorithm based on ear decomposition for testing vertex four-connectivity and for finding all separating triplets in a triconnected graph. The sequential implementation of our algorithm runs in O(n2) time and the parallel implementation runs in O(logn) time using O(n2) processors on a CRCW PRAM, where n is the number of vertices in the graph. This improves previous bounds for the problem for both the sequential and parallel cases. The sequential algorithm is optimal if the input is specified in adjacency matrix form, or if the input graph is dense.
29 citations
TL;DR: In this article, the topological properties of eigenvectors of adjacency matrices of a graph have been analyzed using vertex-signed and edge-signed graphs, where the relative ordering of net signs of edge signed graphs is similar to that of eigvalues of the adjacence matrix.
28 citations
TL;DR: This paper considers elementary squares of any size, and gives procedures for both aspects of the problem: for determining whether two given regions are adjacent, and for finding all the neighbors of different sizes for a given region.
Abstract: A method is presented for determining whether two given regions are adjacent, and for finding all the neighbors of different sizes for a given region. Regions are defined as elementary squares of any size. In a companion paper [2], we introduce the quadcode and discuss its use in representing geometric concepts in the coded image, such as location, distance, and adjacency. In this paper we give a further discussion of adjacency in terms of quadcodes. Gargantini [1] discussed adjacency detection using linear quadtrees. Her discussion was applied to pixels, and a procedure was given to find a pixel's southern neighbor only. This paper considers elementary squares of any size, and gives procedures for both aspects of the problem: for determining whether two given regions are adjacent, and for finding all the neighbors of different sizes for a given region.
28 citations
TL;DR: In this paper, it was shown that in some cases, it is not always possible to satisfy the area constraints in facility layouts, even when the perimeter and rooms must be rectangular, undimensioned floorplans can fit any maximal outerplanar adjacency graph with at most four vertices of degree 2.
Abstract: In facility layouts—the designing of floorplans with certain rooms adjacent to each other—there are often area constraints for the rooms. Robinson and Janjic showed that, if areas are specified for rooms with a given maximal outerplanar adjacency graph, then any convex polygon with the correct area can be divided into convex rooms to satisfy both area and adjacency requirements. If the perimeter and rooms must be rectangular, undimensioned floorplans can be found to fit any maximal outerplanar adjacency graph with at most four vertices of degree 2. It is shown that in some cases it is not always possible to satisfy the area constraints.
27 citations
TL;DR: In this paper, the structural relationship between connected regions of constant grey level (i.e., constant temperature) is described by a region adjacency graph with the position on the graph being determined by the depth of enclosure of the particular atom.
Abstract: The amount of imagery generated by all the various satellite-borne thermal infrared sensors is great and constantly growing. To analyze this imagery manually is tedious and time consuming. The present paper is concerned with automating the extraction of one important, though often weak, type of oceanic feature viz. isolated blob structure. These "blobs" usually correspond to distinct oceanographic features such as eddies or regions of upwelling. The technique proposed to achieve this aim is based on finding the structural relationship between connected regions of constant grey level (i.e., constant temperature). These elementary connected regions are known as atoms. The relationship between atoms is described by a region adjacency graph with the position on the graph being determined by the depth of enclosure of the particular atom. An eddy-like structure is extracted by searching the graph for isolated atoms of high temperature that are enclosed by atoms of lower temperatures (for warm core eddies). Techniques of preprocessing to reduce the search problem to managable proportions and methods to deal with cloud and land "contamination" are also described. The examples given are based on thermal imagery from the Heat Capacity Mapping Mission (HCMM).
24 citations
01 Jun 1987
TL;DR: A class of mesh networks with wrap-around links is obtained from a class of circulant graphs by means of a graph isomorphism, and it is shown that diameter and average distance are simultaneously minimized, implying a minimization of the network communication delays.
Abstract: A class of mesh networks with wrap-around links is obtained from a class of circulant graphs by means of a graph isomorphism. We demonstrate how to obtain, from the adjacency pattern of the graph, simple parameters that serve to construct a planar design of the network. Several performance parameters are evaluated: in particular, we show that diameter and average distance are simultaneously minimized. This implies a minimization of the network communication delays. Due to its easy implementation and good behavior characteristics, the proposed interconnection scheme is appropriate in several architectural environments. Specifically, this topology is suitable as an interconnection subsystem for message passing MIMD architectures, as well as for SIMD machines with a static interconnection scheme. In the particular case of SIMD machines, a comparison is made with the ILLIAC IV-type networks. As a consequence, we propose still another topology, when the number of processing elements is an even power of 2; for this solution, we show that a reduction in the network distances is achieved, without losing speed in performing arbitrary permutations.
01 Jul 1987
TL;DR: This work shows that a 5-colouring of the vertices of an n-vertex planar graph may be computed in O(log n log* n) time by an exclusive-read exclusive-write parallel RAM with O(n/(log nlog* n)) processors.
Abstract: We show that a 5-colouring of the vertices of an n-vertex planar graph may be computed in O(log n log* n) time by an exclusive-read exclusive-write parallel RAM with O(n/(log n log* n)) processors. Our algorithm, while faster than all previously known methods, is at the same time the first parallel 5-colouring algorithm to achieve optimal speedup. It should be emphasized that although input to the algorithm is a planar graph, we do not require a planar embedding to be given as part of the input.
01 Apr 1987
TL;DR: The paper describes the adaptations in the chart parser which was implemented as part of the TENDUMdialogue system and shows that tree-like constituent structures with discontinuities can be given a precise definition which makes them just as acceptable for syntactic representation as ordinary trees.
Abstract: This paper discusses the consequences of allowing discontinuous constituents in syntactic representions and phrase-structure rules, and the resulting complications for a standard parser of phrase-structure grammar.It is argued, first, that discontinuous constituents seem inevitable in a phrase-structure grammar which is acceptable from a semantic point of view. It is shown that tree-like constituent structures with discontinuities can be given a precise definition which makes them just as acceptable for syntactic representation as ordinary trees. However, the formulation of phrase-structure rules that generate such structures entails quite intricate problems. The notions of linear precedence and adjacency are reexamined, and the concept of "n-place adjacency sequence" is introduced. Finally, the resulting form of phrase-structure grammar, called "Discontinuous Phrase-Structure Grammar", is shown to be parsable by an algorithm for context-free parsing with relatively minor adaptations. The paper describes the adaptations in the chart parser which was implemented as part of the TENDUMdialogue system.
01 Oct 1987
TL;DR: This paper describes using adjacency lists to incrementally generate design rule spacing constraints, generating the smallest complete set of constraints for a design, yielding fast compaction, and is as fast or faster than ordinary constraint generation methods even when the incremental features are not used.
Abstract: This paper describes using adjacency lists to incrementally generate design rule spacing constraints. The algorithm generates the smallest complete set of constraints for a design, yielding fast compaction, and is as fast or faster than ordinary constraint generation methods even when the incremental features are not used. The adjacency list data structure allows one to very quickly move, insert or delete objects and generate an updated set of constraints.
25 Feb 1987
TL;DR: The algorithms presented provide the basis for an efficient navigation sytem for an autonomous robot working in an unexplored terrain and the time and space complexities of the various algorithms are discussed.
Abstract: Recently an approach to the problem of robot navigation in an unexplored terrain was develped by Iyengar, et al, which involves concepts of learning. The method proposed involves representing the terrain as a spatial graph which is updated as the robot undertakes a number of goal-directed traversals. The current paper focuses on the implementation of the spatial graph data structure and Parallel Algorithms needed to maintain the data structure. A modified adjacency list data structure is proposed for representing the spatial graph of the terrain. The model of computation being used is the multiple instruction stream multiple data stream shared memory model MIMD-SMM. The parallel algorithms required to implement the navigation technique (described in the previously mentioned paper) using the modified adjacency list data structure are presented and the time and space complexities of the various algorithms are discussed. The algorithms presented provide the basis for an efficient navigation sytem for an autonomous robot working in an unexplored terrain.
01 Apr 1987
TL;DR: In this paper, population density is equalized while preserving adjacency relationships, so that clusters of cases can be easily recognized and their statistical significance measured using a density-equalizing computer algorithm.
Abstract: To analyze geographic clusters of disease, one must consider varying population density Customary methods, for example calculation of rates for subregions, are unsatisfactory: if subregions are too large, geographic detail is lost; if too small, stable rates cannot be calculated In either case, adjacency relationships among cases are not easily analyzed The usual difficulties are avoided by using an innovative projection technique On a transformed map, population density is equalized while preserving adjacency relationships, so that clusters of cases can be easily recognized and their statistical significance measured A density-equalizing computer algorithm is briefly described, and its use illustrated in representative applications 11 refs, 30 figs