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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

Abstract: A method of building a three-dimensional model of a rigid object using information from many views is described. Planar and quadric surface primitives describe the object's surface in an object-centered reference frame. The extent of a primitive is defined by the intersection of the primitive with its neighbors. An edge graph defined by these intersections implicitly expresses spatial relationships between surface primitives. The model builder's input consists of groups of data points corresponding to different views. Each data point contains spatial and orientation information about the object's surface at a discrete location. A set of registered arrays is used to summarize input information in local areas. Mathematical principles from differential geometry are applied to determine local surface properties. A region-growing technique is applied to this information to identify data points which then are represented by a surface primitive. Edges and corners are computed based on the intersections of surface primitives. The results from the analysis of the various views are transformed to a common, arbitrary reference frame for integration into a global model. The final object-centered reference frame is established based on the center of gravity and moments of inertia of the object as determined from the complete model. The goal of model building has applications in the fields of pattern recognition, computer vision, robotics, computer-aided design and computer-aided manufacturing. A model using surface primitives appears as a natural first step in describing an object because surfaces are obvious visual features. The strengths and weaknesses of this surface model are explored.

Abstract: We define a series of locking protocols for database systems that all have three main features: freedom from deadlock, multiple granularity, and support for general collections of locking primitives. A rooted directed acyclic graph is used to represent multiple granularities, as in System R. Deadlock freedom is guaranteed by extending the System R protocol to require locks on edges of the graph in addition to the locks required on nodes.

Abstract: A representation by a complex power-complex voltage (S-E) graph is introduced for power networks in place of the conventional complex current- complex voltage (I-E) graph. In the S-E graph transmission lines flows are separated into transmitted and loss power. This leads to the formulation of the load flow algorithm based on dividing the network into a tree and a cotree and alternating flow computations on the cotree with voltage update along the tree either as a Jacobi or a Gauss-Seidel algorithm. The algorithm proves to be effective with consistent convergence. It handles constrains smoothly and is fully attuned to computing load flows on the compound HV-AC-DC network. Parallel processing can be applied with essentially no idle time. Proof of convergence was attained.

Abstract: This paper is a written version of the overview lecture on “Concurrency in Graph Grammars” given at the “2nd International Workshop on Graph Grammars and their Applications to Computer Science, 1982”. The intention of that lecture and this paper is to show that a number of results in the transformational theory of graph grammars can be considered already as contributions towards a theory of concurrency in graph grammars. Simulations of Petri nets within graph grammars are reviewed and simulations of algebraic specifications within graph grammars are introduced to cover also abstract data type concepts. More general concepts of concurrency are considered to be studied in the framework of graph grammars which go essentially beyond those in Petri nets. Finally it is proposed to combine the new approach of Ugo Montanari for synchronization with the aspects of concurrency reviewed above to obtain a graph grammar based model for concurrent and distributed systems.

Abstract: In this paper we consider a resource allocation problem which is local in the sense that the maximum number of users competing for a particular resource at any time instant is bounded and also at any time instant the maximum number of resources that a user is willing to get is bounded. The problem may be viewed as that of achieving matchings in dynamically changing hypergraphs, via a distributed algorithm. We show that this problem is related to the fundamental problem of handshake communication (which can be viewed as achieving matchings in a dynamically changing graph, via distributed algorithms) in that an efficient solution to each of them implies an efficient solution to the other. We provide real-time solutions to the resource allocation problem (that is, we give distributed algorithms with real time response). We make essential use of probabilistic techniques as first used by [Rabin, 80b], where processes are allowed to make independent probabilistic choices. On the other hand, no probability assumptions about the system behavior are made. One of our solutions assumes the existence of an underlying real-time handshake communication system, as described in [Reif, Spirakis, 81]. Our other solution is based on efficient synchronization by flag variables, which are written only by one process and read by at most one other process. The special case of equi-speed processes is first examined. Then we generalize to asynchronous processes. Applications are made to dining philosophers, scheduling and two-phase locking in databases.