Showing papers on "Graph (abstract data type) published in 1982"

Register allocation & spilling via graph coloring

Abstract: In a previous paper we reported the successful use of graph coloring techniques for doing global register allocation in an experimental PL/I optimizing compiler. When the compiler cannot color the register conflict graph with a number of colors equal to the number of available machine registers, it must add code to spill and reload registers to and from storage. Previously the compiler produced spill code whose quality sometimes left much to be desired, and the ad hoe techniques used took considerable amounts of compile time. We have now discovered how to extend the graph coloring approach so that it naturally solves the spilling problem. Spill decisions are now made on the basis of the register conflict graph and cost estimates of the value of keeping the result of a computation in a register rather than in storage. This new approach produces better object code and takes much less compile time.

An Algorithm for Partitioning the Nodes of a Graph

Abstract: Let $G = \{ N,E \}$ be an undirected graph having nodes N and edges E We consider the problem of partitioning N into k disjoint subsets $N_1 , \cdots ,N_k $ of given sizes $m_1 , \cdots ,m_k $, respectively, in such a way that the number of edges in E that connect different subsets is minimal We obtain a heuristic solution from the solution of a linear programming transportation problem

Common expression analysis in database applications

Abstract: Independent optimization of database requests overlooks potential savings which can be achieved when they are optimized collectively. An intuitive model for queries called the query graph supports common expression detection for optimization of a stream of requests. We describe how ad hoc query processing can be improved using intermediate results and answers produced from earlier queries, without significantly impacting processing costs when no common expressions are found. We have written a Pascal program, COMMON, which implements a variation of the algorithm which we describe.

Super-combinators a new implementation method for applicative languages

Abstract: There is a growing interest nowadays in functional programming languages and systems, and in special hardware for executing them. Many of these implementations are based on a system called graph reduction (GR), in which a program is represented as a graph which is transformed, or reduced, by the machine until it represents the desired answer. The various graph reduction implementations differ in the structure of the “machine code” (the program graph) and the compilation algorithms necessary to produce it from a source language. This paper describes a new implementation method using super-combinators which is apparently more efficient than its predecessors. Consideration of the new method also helps clarify the relationships between several other graph-reduction schemes. This paper is necessarily brief, but a fuller account can be found in [Hughes].The simplest machine language we shall consider consists of constants combined by function application. This is the language of constant applicative forms (cafs). Some of the constants are basic functions.

Algorithms for Generating Fundamental Cycles in a Graph

Abstract: The following problem is considered: Given an undirected, connected graph G, find a spanning tree in G such that the sum of the lengths of the fundamental cycles (with respect to this tree) is minimum. This problem, besides being interesting in its own right, is useful in a variety of situations It is shown that this problem is NP-complete. A number of polynomial-time, heuristic algorithms which yield "good" suboptimal solutions are presented and their performances are discussed. Finally, it is shown that for regular graphs of order n the expected value of the total length of a minimum fundamentalcycle set does not exceed O(n2).

Power System Topological Observability Using a Direct Graph-Theoretic Approach

Abstract: The topological observability of a Power System State Estimation (PSSE) problem is considered. The PSSE observability is decoupled into two separate problems using the well-known P-?/Q-V decouple characteristic of power systems. Using a linear decoupled model for the measurements, the proposed method tries to find an observable spanning tree of the P-?measurement graph (and subsequently for the Q-V measurement graph) using an algorithm for the search of matroid intersections. The method is first applied to six well- known examples of the technical literature, and then is used to study six different cases of a realistic system comprising 121 buses.

A network flow solution to some nonlinear 0‐1 programming problems, with applications to graph theory

Abstract: A network flow technique is used to solve the unconstrained nonlinear 0-1 programming problem, which is maximizing the ratio of two polynomials, assuming that all the nonlinear coefficients in the numerator are non-negative and all the nonlinear coefficients in the denominator are nonpositive. Two examples are an investment selection problem to maximize the rate of return, and a decomposition approach to a scheduling problem studied by Sidney and Lawler. The proposed algorithm requires the solution of a sequence of minimum-cut problems in a related network, and can be extended to some more general problems of the same type. This approach is also applied to find the density of a graph (the maximum ratio, among its subgraphs, of the number of edges to the number of nodes) and its arboricity, for which polynomial algorithms are described. It is also useful in providing a bounding scheme for the maximum-clique and vertex packing problems.

Parallel algorithms in graph theory: planarity testing*

Abstract: We present efficient $(O(\log ^2 n))$ parallel algorithms for two classical graph problems: planarity testing and finding triconnected components. The algorithms use only a polynomial number of processors. Previous algorithms used $\Omega (n)$ operations, regardless of the number of available processors.

Disjoint paths in a rectilinear grid

Abstract: We give a good characterization and a good algorithm for a special case of the integral multicommodity flow problem when the graph is defined by a rectangle on a rectilinear grid. The problem was raised by engineers motivated by some basic questions of constructing printed circuit boards.

Attributed graph grammars for graphics

Abstract: This paper presents a formalization of the notion graphic. A graphic is considered to consist of an ordinary graph describing the overall structure and a set of attributes describing the shape, placement, etc. of the nodes and edges of the underlying graph. The formal handling of graphics is done by attributing the rules of graph grammars and by passing the attributes up and down the derivation tree of the graphic.

Protocols for Deadlock Detection in Distributed Database Systems

Abstract: In distributed databases, deadlocks may occur due to conflicts in data file lockings A system is in a deadlock if and only if there is a directed cycle in its demand graph. However, due to the inherent communication delay in a distributed system, it is not easy to construct a consistent demand graph for a distributed system. In this paper, three deadlock detection protocols are discussed. The first protocol uses two communication phases. The second protocol uses a single communication phase. Based on the second protocol, a one-phase hierarchical deadlock detection protocol is developed.

The graph metric for unstable plants and robustness estimates for feedback stability

Abstract: In this paper, a "graph metric" is defined that provides a measure of the distance between unstable multivariable plants. The graph metric induces a "graph topology" on unstable plants, which is the weakest possible topology in which feedback stability is robust. Using the graph metric, it is possible to derive estimates for the robustness of feedback stability without assuming that the perturbed and unperturbed plants have the same number of RHP poles. If the perturbed and unperturbed systems have the same RHP poles, then it is possible to obtain necessary and sufficient conditions for robustness with respect to a given class of perturbations. As an application of these results, the design of stabilizing controllers for unstable singularly perturbed systems is studied.

Determination of All Minimal Cut-Sets between a Vertex Pair in an Undirected Graph

Abstract: An efficient enumeration algorithm generates all minimal cut-sets separating a special vertex pair in an undirected graph. The algorithm is based on a blocking mechanism that guarantees that every minimal cut-set between the two specified vertices is generated exactly once. The algorithm is intended for computer implementation, and computational times are provided.

Graph-theoretic approach to controllability and localizability of decentralized control systems

Abstract: The controllability and the localizability problems are considered under the decentralized information structure using some concepts from graph theory. First of all, the information structure graph is introduced for a decentralized control system based upon local output controllability, matrices between stations when a local output feedback law is applied, and some invariant properties of the graph with respect to local output feedback laws are driven. Then by using these results, necessary and sufficient conditions of controllability under decentralized information structure are obtained. Also obtained are several conditions for localizability, of decentralized control systems, which is newly introduced in the present paper as an extended concept of a class of disturbance localization and decoupling for centralized systems.

An architecture for query optimization

Abstract: We describe an optimizer for relational queries to databases stored as flat files and Codasyl networks. We include sophisticated manipulations on a broad range of direct access structures (DAS's). To achieve this with minimum additional code, we allow operations like sort, scan, and join to apply to DAS's, and categorize indexes and other DAS's in terms of the operations which can be performed on them. Our storage model, based on indivisible units of access and a small set of associated physical operators, provides a uniform interface to both relational and Codasyl storage mechanisms. The optimizer derives a sequence of internal data structures at successively more detailed levels. For a given query, a graph representing an overview of alternative joins is constructed, and then used to derive a physical graph which considers the physical attributes (location and sort order) of the data objects involved. Using cost predictions and other heuristics, the optimizer prunes the physical graph to produce a final access strategy tree. This layered approach and reliance on primitive operators make explicit (and permit changes to) the universe of possible strategies for the query at hand, and ease extension of the optimizer to new storage structures.

Optimum matching forests I: Special weights

Abstract: We introduce the concept of matching forests as a generalization of branchings in a directed graph and matchings in an undirected graph. Given special weights on the edges of a mixed graph, we present an efficient algorithm for finding an optimum weight-sum matching forest. The algorithm is a careful application of known branching and matching algorithms. The maximum cardinality matching forest problem is solved as a special case.

Succinct representation of graphs

Abstract: This work presents a different approach to the continuing work done in the development of efficient algorithms for the solution of graph problems. While until now the main effort has been directed towards designing more efficient algorithms, we try to get a better solution by changing the graph representation. We suggest a new model for graph representation, which we named Graph Construction Representation. The new model proved to have two significant advantages over the conventional graph representations: (1) For many graphs, this model will use less space, or in other words will have a "succinct" representation. (2) We developed several algorithms which accept the new model as input. The time complexity for those algorithms when applied to graphs which are represented "succinctly" is improved in comparison with the best known algorithm. In this thesis the Graph Construction Representation is investigated. For many graph families it is shown how they are represented using this model. Bounds on the size of the representation are given. Several algorithms for checking graph properties are described, among them "Connectivity", "Has a Triangle?" and "Maximum Independent Set". We identify problems which are still open concerning the representation of graphs which are related to a graph already succinctly represented. We have only partial answers for these questions. We also present another graph representation, which was named the Small Circuit Representation, for which we prove that checking many graph properties is hard.

Graph Grammars as a generative tool in image understanding

Abstract: Attributed programmed graph grammars are introduced in this paper and their application to a particular problem in image understanding, the understanding of schematic drawings like circuit diagrams and flowcharts, is described.

Comment on "Reliability Evaluation of a Flow Network

Abstract: The method of Lee and the simple application of graph theory seem to give different answers for flow networks. Lee's method is correct. The method whereby graph theory can be extended to give correct results is explained.

Optimal implementation of signal flow graphs on synchronous multiprocessors.

Abstract: A primary goal of this research is to develop procedures for automatically generating optimal multiprocessor signal flow graph implementations from a simple, nonparallel representation of the algorithm to be implemented An appropriate algorithmic representation might be a set of difference equations or a matrix presentation of the signal flow graph The techniques studied are constrained only by the synchrony of the system, the existence of a skewed single instruction multiple data (SSIMD) mode, and the use of identical constituent processors 6 references

Finding a minimum equivalent graph of a digraph

Abstract: The problem considered is that of removing the maximum number of edges from a digraph without affecting its reachability properties. The worst-case performance of algorithms from the related literature is analyzed; it is found that Hsu's method contains some mistakes. A new algorithm is presented, based on a reduction procedure and on a branch and bound search; its efficiency is studied both theoretically and through computational experiments.