Showing papers on "Graph (abstract data type) published in 1983"
24 Jan 1983
TL;DR: It is argued that this technique can provide a practical alternative to manual proof construction or use of a mechanical theorem prover for verifying many finite state concurrent systems.
Abstract: We give an efficient procedure for verifying that a finite state concurrent system meets a specification expressed in a (propositional) branching-time temporal logic. Our algorithm has complexity linear in both the size of the specification and the size of the global transition graph for the concurrent system. We also show how the logic and our algorithm can be modified to handle fairness. We argue that this technique can provide a practical alternative to manual proof construction or use of a mechanical theorem prover for verifying many finite state concurrent systems.
484 citations
TL;DR: The algebraic definitions presented here are motivated by the search for an adequate formalization of the concepts of social roles as regularities in social network patterns and represent significant homomorphic reductions of social networks which are possible using these defimtions to capture the role structure of a network.
367 citations
01 Jan 1983
292 citations
TL;DR: In this article, it was shown that if a graph G^n has n vertices and 12nlogn+12nogn+cn edges, then it is Hamiltonian with probability P"c tending to exp exp exp(-2c) as n->~.
278 citations
TL;DR: Two graph theoretic models are introduced that provide a uniform procedure for analyzing 2n-input/2n-output Multistage Interconnection Networks (MIN's), implemented with 2- input/2-output Switching Elements (SE's) and satisfying a characteristics called the "buddy property."
Abstract: This paper introduces two graph theoretic models that provide a uniform procedure for analyzing 2n-input/2n-output Multistage Interconnection Networks (MIN's), implemented with 2-input/2-output Switching Elements (SE's) and satisfying a characteristics called the "buddy property." These models show that all such n-stage MIN's are topologically equivalent and hence prove that one MIN can be implemented from integrated circuits designed for another MIN. The proposed techniques also allow identical modeling and comparison of permutation capabilities of n-stage MIN's and other link-controlled networks like augmented data manipulator and SW Banyan Network and hence, allows comparison of their permutation. In the case of any conflict in the MIN, an upper bound for the required number of passes has been obtained.
203 citations
01 Dec 1983
TL;DR: An analogy between linear systems and a class of discrete-event systems is developed that can be viewed as linear, in the sense of an appropriate algebra, and the potentiality of this approach for the performance evaluation of repetitive production processes is illustrated.
Abstract: A discrete-event system is a system whose behavior can be described by means of a set of time-consuming activities, performed according to a prescribed ordering. Events correspond to starting or ending some activity. An analogy between linear systems and a class of discrete-event systems is developed. Following this analogy, such discrete-event systems can be viewed as linear, in the sense of an appropriate algebra. The periodical behavior of closed discrete-event systems, i.e. involving a set of repeatedly performed activities, can be totally characterized by solving an eigenvalue and eigenvector equation in this algebra. This problem is numerically solved by an efficient algorithm which basically consists in finding the shortest paths from one node to all other nodes in a graph. The potentiality of this approach for the performance evaluation of repetitive production processes is illustrated on an example.
174 citations
01 Jan 1983
155 citations
TL;DR: The OTC and OTN can be looked upon as general purpose parallel processors since a number of other problems such as sorting and DFT can be solved on them with an area * time2 performance matching that of other networks.
Abstract: In this paper we describe two interconnection networks for parallel processing, namely the orthogonal trees network and the orthogonal tree cycles (OTN and OTC). Both networks are suitable for VISI implementation and have been analyzed using Thompson's model of VLSI. While the OTN and OTC have time performances similar to fast networks such as the perfect shuffle network (PSN), the cube comnected cycles (CCC), etc., they have substantially better area * time2 performances for a number of matrix and graph problems. For instance, the connected components and a minimal spanning tree of an undirected N-vertex graph can be found in 0(log4 N) time on the OTC with an area * time2 performance of 0(N2 log8 N) and 0(N2 log9 N) respectively. This is asymptoticaly much better than the performances of the CCC, PSN and Mesh. The OTC and OTN can be looked upon as general purpose parallel processors since a number of other problems such as sorting and DFT can be solved on them with an area * time2 performance matching that of other networks. Finally, programming the OTN and OTC is simple and they are also amenable to pipelining a series of problems.
116 citations
TL;DR: It is proved that every bidirected graph which can be provided with a nowhere-zero integral flow can also be providedWith absolute values less than 216.
102 citations
TL;DR: A graph-theoretic approach for the representation of functional dependenoes in relauonal databases is introduced and applied in the construction of algorithms for manipulating dependencies, which leads to simpler proofs and, in some cases, more efficient algorithms than in the current literature.
Abstract: . A graph-theoretic approach for the representation of functional dependenoes in relauonal databases is introduced and applied in the construction of algorithms for manipulating dependencies. This approach allows a homogeneous treatment of several problems (closure, minimization, etc.), which leads to simpler proofs and, m some cases, more efficient algorithms than in the current literature. Categories and Subject Descriptors: F.2.2 [Analysis of Algorithms and Problem Complexity]: Nonnumencal Algorithms and Problems--computations on d, screte structures; G.2.2 [Diserete Mathematics]: Graph Theory--graph algorithms; H.2.1 [Database Management]: Logical Design-normal forms; schema and subschema General Terms: Algorithms, Design, Management, Theory Additional Key Words and Phrases: Closure, computational complexity, functional dependency, FD- graph, minimal coverings, relational database 1. Introduction
101 citations
07 Nov 1983
TL;DR: This work presents efficient algorithms for network problems that work by scaling the numeric parameters, and gives simple algorithms that match the best time bounds for shortest paths on a directed graph with nonnegative lengths and maximum value network flow.
Abstract: A network is a graph with numeric parameters such as edge lengths, capacities, costs, etc. We present efficient algorithms for network problems that work by scaling the numeric parameters. Scaling takes advantage of efficient nonnumeric algorithms such as the Hopcroft-Karp matching algorithm. Let n, m and N denote the number of vertices, number of edges, and largest numeric parameter of the network, respectively; assume all numeric parameters are integers. A scaling algorithm for maximum weight matching on a bipartite graph runs in O(n3/4 m log N) time. This can improve the traditional Hungarian method which runs in O(n m log n) time. This result gives similar improvements for the following problems: single-source shortest paths for arbitrary edge lengths (Bellman's algorithm); maximum weight degree-constrained subgraph; minimum cost flow in a 0-1 network (Edmonds and Karp). Scaling also gives simple algorithms that match the best time bounds (when log N = O(log n)) for shortest paths on a directed graph with nonnegative lengths (Dijkstra's algorithm) and maximum value network flow (Sleator and Tarjan).
TL;DR: This paper shows how the application of fuzzy sets to such problems can yield quasi-deterministic results obtained from imprecise Input data.
Abstract: Currently used network planning techniques, such as PERT/CPM and their derivatives, assume that, in a graph of known structure, the duration of its activities is known either with certitude or at least with some probability. However, in many applications the structure of the graph and the duration of its activities are imprecise. This paper shows how the application of fuzzy sets to such problems can yield quasi-deterministic results obtained from imprecise Input data.
TL;DR: An algorithm based on region growing is investigated in terms of its efficiency in segmenting a set of points in 3-D space into planar faces based on information on the neighborhood structure of the points in the form of a spatial proximity graph.
Abstract: The representation of 3-D objects is an important step in solving many problems in scene analysis. One of the most successful techniques is that based on the surfaces of objects. We describe several methods for obtaining such surface representations from various types of intrinsic images. In particular, previous work is reviewed and an algorithm based on region growing is investigated in terms of its efficiency in segmenting a set of points in 3-D space into planar faces. Information on the neighborhood structure of the points in the form of a spatial proximity graph is used to direct the segmentation. Applications to industrial objects are demonstrated.
01 Jan 1983
TL;DR: The Rain space, a framework treating the fuzzy subsets as random subsets will be introduced and a correspondence theorem which combines the falling random subset and the measurable fuzzy subset is given.
Abstract: In this paper we shall discuss some problems concerning the fuzzy statistics and the random subsets. The Rain space, a framework treating the fuzzy subsets as random subsets will be introduced. In this space, the measurability of random subsets is equivalent to the strong measurability. Applying the graph of random subsets we will give a correspondence theorem which combines the falling random subsets and the measurable fuzzy subsets. Finally, we will discuss the operations of fuzzy subsets, some interesting results will be found.
Proceedings Article•
08 Aug 1983TL;DR: The methodology to deal with the behavior of a dynamical system such as plant controllers in the framework of Temporal Logic is described and an automatic synthesis of control rules can be reduced to a simple decision procedure on the w -graph.
Abstract: This paper describes the methodology to deal with the behavior of a dynamical system such as plant controllers in the framework of Temporal Logic. Many important concepts of the dynamical system like stability or observability are represented in this framework. As a reasoning method, we present an w -graph approach which enables us to represent the dynamical behavior of a given system, and an automatic synthesis of control rules can be reduced to a simple decision procedure on the w -graph. Moreover, the typical reasoning about the time-dependent system such as a causal argument or a qualitative simulation can be also treated on the w -graph in the same way.
Proceedings Article•
27 Sep 1983
TL;DR: A logical model (called GRASS) for representing both the properties of a Statistical Data Base and the tables view, which represent the peculiar reality of statistical user is proposed.
Abstract: In this paper the Authors propose a logical model (called GRASS) for representing both the properties of a Statistical Data Base (S. D. B.) and the tables view, which represent the peculiar reality of statistical user.The proposed model consists of a marked, labeled, direct, connected, acyclic, partially ordered graph. For this graph nodes semantics and connection andbranchingrules are provided. A cognitive and selective approach to how navigate through category attributes and summary data are given too. Finally, some facilities of the model are discussed and a comment is made.
TL;DR: This work extends to the multi-constrained, unweighted case, the analysis that was already made in a previous work for the one-conStrained, weighted case of undirected spanning tree problems from the viewpoint of their computational complexity.
Proceedings Article•
08 Aug 1983
TL;DR: The mathematical structuring tool used is the decomposition of a graph into its k-connected components, which allows the robot to improve navigation procedures and to recognize some concepts, such as a door, a room, or a corridor.
Abstract: We present here a method for providing a mobile robot with learning capabilities. The method is based on a model of the environment with several hierarchical levels organized by degree of abstraction. The mathematical structuring tool used is the decomposition of a graph into its k-connected components (k=2 and k=3). This structure allows the robot to improve navigation procedures and to recognize some concepts, such as a door, a room, or a corridor.
TL;DR: In this paper, a numerical method for the dynamic simulation of towed cables is presented, where the cable is loaded by fluid drag, tension, gravity and buoyancy, including the effects of weights and floats.
TL;DR: In this article, a new approach is presented, in which, having associated a directed graph with the matrix to be identified, a set of "forms" is defined which are functions of the elements of matrix itself.
Abstract: This work deals with the problem of the a priori identifiability of compartmental systems from input-output experiments. A new approach is presented, in which, having associated a directed graph with the matrix to be identified, a set of “forms” is defined which are functions of the elements of matrix itself. It is shown how, by exploiting the topological properties of the graph and its subgraphs, the problem can be simplified into one of smaller dimensions. Examples are provided to illustrate this new approach.
TL;DR: The present paper gives a simpler algorithm with the faster running time of O(m log n) time for hierarchically decomposing a directed n-vertex, m-edge graph with weighted edges into strong components.
TL;DR: Let G = (V, A) be a directed graph (or digraph), where V is the set of the n ver t ices and A is theset o f the m arcs (v,, vj) in G.
Abstract: Let G = (V, A) be a directed graph (or digraph), where V {vl, v2 . . . . . v ,} is the set of the n ver t ices and A is the set o f the m arcs (v,, vj) in G. A Hamiltonian circuit in G is a p e r m u t a t i o n (s,) o f the ver t ices such t h a t (vs,, v,,+,) E A for t = 1, . . . , n 1 and (v~,,, v,,) ~ A. T h e p rob lem of f inding one or m o r e H a m i l t o n i a n circui ts in a given g r a p h (or a l te rna t ive ly of de te rmin ing t h a t the g raph does no t possess H a m i l t o n i a n circuits) is k n o w n to be long to the class of the NP-complete problems, so exac t e n u m e r a t i v e a lgor i thms or heur is t ic t echn iques are genera l ly used for its solut ion. Th i s pape r presents a p r o g r a m for solving the fol lowing genera l p rob lem, e i ther exact ly or heurist ical ly:
TL;DR: It is shown that for d-way shuffle graphs all oblivious algorithms for realizing permutations in logarithmic time send packets along routes twice as long as the diameter of the graph.
Abstract: It is shown that for d-way shuffle graphs all oblivious algorithms for realizing permutations in logarithmic time send packets along routes twice as long as the diameter of the graph. This confirms the optimality of the strategy that sends packets to random nodes in a first phase and to the correct destinations in the second. For the shuffle-exchange graph the corresponding route length is shown to be strictly longer than for the 2-way shuffle.
18 Jul 1983
TL;DR: A global compaction algorithm which can produce efficient microprograms with respect to both space and time and depends upon a generalized data dependency graph (GDDG), which can integratedly express the concurrency of microorders and their mobility past the boundaries of basic blocks, as well as the control flow for a microprogram.
Abstract: This paper describes a global compaction algorithm which can produce efficient microprograms with respect to both space and time The algorithm depends upon a generalized data dependency graph (GDDG), which can integratedly express the concurrency of microorders and their mobility past the boundaries of basic blocks, as well as the control flow for a microprogram In the algorithm an initial GDDG is first built up from a source microprogram consisting of a sequence of microorders, and this is transformed by repeated application of a set of microscopic transformation rules to the graph's edges until all of them have been examined Then microorders are packed into microinstruction fields so that the more frequently executed basic blocks may contain as few microinstructions as possible The intrinsic nature of the control flow's joins and forks allows determination of which basic block should accommodate those microorders that can be placed in more than one basic block
01 Oct 1983
TL;DR: An approach of decomposition is proposed through which the protocol graph can be partitioned into subgraphs each having a unique entry node and zero or more exit nodes and it is shown that the entire protocol graph will operate correctly.
Abstract: Finite state automata have been applied with success to the modeling of Computer Network Protocols The interaction of finite state machines can be very complex especially if the protocol involves a large number of states To counteract the complexity of analysis and design, we propose an approach of decomposition Through this approach, the protocol graph can be partitioned into subgraphs each having a unique entry node and zero or more exit nodes The exit nodes of one subgraph can be connected only to the entry nodes of other subgraphs From the standpoint of protocol analysis, the correctness of the entire protocol graph can be inferred from the correctness of individual protocol subgraphs From the standpoint of protocol design, the individual protocol subgraphs can be designed to correspond to different phases of the protocol If the individual protocol subgraphs are designed correctly and the connections between subgraphs conform to the structure discussed above, then we show that the entire protocol graph will operate correctly
TL;DR: In this article, the authors locate a sharp threshold for the property of having a hamiltonian path in the scale of random graph spaces, where the ap-band across which the asymptotic probability of Q jumps from 0 to 1 is defined.
Abstract: A threshold for a graph propertyQ in the scale of random graph spacesG
n,p
is ap-band across which the asymptotic probability ofQ jumps from 0 to 1. We locate a sharp threshold for the property of having a hamiltonian path.
TL;DR: The use of the decomposition tree for reliability computation purposes is introduced, a general algorithm based on the tree is presented, and its application to the problems named above are demonstrated, as well as to the problem of feasible shortest path.
Abstract: Available algorithms for measures of network reliability require computation time f(n) where f is at least exponential in n, the number of failure-prone elements in the system. Modularization is a familiar method of decomposing a network reliability problem into a set of subproblems. This decomposition reduces required computation time from f(n) to a sum of f(ni), ni < n, usually a considerable saving. For a 2-terminal communication network, the decomposition tree of a network provides the identity of the modules and an easily read map of the relations among them. The decomposition tree is derived by finding the triconnected components of the underlying graph. Reducing computation time by finding and analyzing the triconnected components of a network has been proposed for the reliability problems of 2-terminal communication, all-terminal communication, and feasible transportation flow. This paper introduces the use of the decomposition tree for reliability computation purposes, presents a general algorithm based on the tree, and demonstrates its application to the problems named above, as well as to the problem of feasible shortest path.