Showing papers on "Graph (abstract data type) published in 1996"

Points-to analysis in almost linear time

Abstract: We present an interprocedural flow-insensitive points-to analysis based on type inference methods with an almost linear time cost complexity To our knowledge, this is the asymptotically fastest non-trivial interprocedural points-to analysis algorithm yet described The algorithm is based on a non-standard type system. The type inferred for any variable represents a set of locations and includes a type which in turn represents a set of locations possibly pointed to by the variable. The type inferred for a function variable represents a set of functions It may point to and includes a type signature for these functions The results are equivalent to those of a flow-insensitive alias analysis (and control flow analysis) that assumes alias relations are reflexive and transitive.This work makes three contributions. The first is a type system for describing a universally valid storage shape graph for a program in linear space. The second is a constraint system which often leads to better results than the "obvious" constraint system for the given type system The third is an almost linear time algorithm for points-to analysis by solving a constraint system.

Property Testing and its connection to Learning and Approximation

Abstract: In this paper, we consider the question of determining whether a function f has property P or is e-far from any function with property P. A property testing algorithm is given a sample of the value of f on instances drawn according to some distribution. In some cases, it is also allowed to query f on instances of its choice. We study this question for different properties and establish some connections to problems in learning theory and approximation.In particular, we focus our attention on testing graph properties. Given access to a graph G in the form of being able to query whether an edge exists or not between a pair of vertices, we devise algorithms to test whether the underlying graph has properties such as being bipartite, k-Colorable, or having a p-Clique (clique of density p with respect to the vertex set). Our graph property testing algorithms are probabilistic and make assertions that are correct with high probability, while making a number of queries that is independent of the size of the graph. Moreover, the property testing algorithms can be used to efficiently (i.e., in time linear in the number of vertices) construct partitions of the graph that correspond to the property being tested, if it holds for the input graph.

A new approach to the minimum cut problem

Abstract: This paper present a new approach to finding minimum cuts in undirected graphs. The fundamental principle is simple: the edges in a graph's minimum cut form an extremely small fraction of the graph's edges. Using this idea, we give a randomized, strongly polynomial algorithm that finds the minimum cut in an arbitrarily weighted undirected graph with high probability. The algorithm runs in O(n2log3n) time, a significant improvement over the previous O˜(mn) time bounds based on maximum flows. It is simple and intuitive and uses no complex data structures. Our algorithm can be parallelized to run in RNC with n2 processors; this gives the first proof that the minimum cut problem can be solved in RNC. The algorithm does more than find a single minimum cut; it finds all of them.With minor modifications, our algorithm solves two other problems of interest. Our algorithm finds all cuts with value within a multiplicative factor of a of the minimum cut's in expected O˜(n2a) time, or in RNC with n2a processors. The problem of finding a minimum multiway cut of graph into r pieces is solved in expected O˜(n2(r-1)) time, or in RNC with n2(r-1) processors. The “trace” of the algorithm's execution on these two problems forms a new compact data structure for representing all small cuts and all multiway cuts in a graph. This data structure can be efficiently transformed into the more standard cactus representing for minimum cuts.

The symbolic model-checking for real-time systems

Abstract: It is important to verify timing conditions in real time systems. In particular, symbolic model checking is promising for verifying a large system. But in dense time models, symbolic model checking based on BDD causes the state explosion problem because of generating a region graph from the specification. We propose symbolic model checking based on BDD in a dense time model, which does not use a region graph. In our proposed symbolic model checker, we represent state spaces by both BDD and DBM (Difference Bound Matrices). We have realized an effective symbolic model checker based on BDD in dense time model with the proposed method.

The hippocampus as a cognitive graph.

Abstract: A theory of cognitive mapping is developed that depends only on accepted properties of hippocampal function, namely, long-term potentiation, the place cell phenomenon, and the associative or recurrent connections made among CA3 pyramidal cells. It is proposed that the distance between the firing fields of connected pairs of CA3 place cells is encoded as synaptic resistance (reciprocal synaptic strength). The encoding occurs because pairs of cells with coincident or overlapping fields will tend to fire together in time, thereby causing a decrease in synaptic resistance via long-term potentiation; in contrast, cells with widely separated fields will tend never to fire together, causing no change or perhaps (via long-term depression) an increase in synaptic resistance. A network whose connection pattern mimics that of CA3 and whose connection weights are proportional to synaptic resistance can be formally treated as a weighted, directed graph. In such a graph, a "node" is assigned to each CA3 cell and two nodes are connected by a "directed edge" if and only if the two corresponding cells are connected by a synapse. Weighted, directed graphs can be searched for an optimal path between any pair of nodes with standard algorithms. Here, we are interested in finding the path along which the sum of the synaptic resistances from one cell to another is minimal. Since each cell is a place cell, such a path also corresponds to a path in two-dimensional space. Our basic finding is that minimizing the sum of the synaptic resistances along a path in neural space yields the shortest (optimal) path in unobstructed two-dimensional space, so long as the connectivity of the network is great enough. In addition to being able to find geodesics in unobstructed space, the same network enables solutions to the "detour" and "shortcut" problems, in which it is necessary to find an optimal path around a newly introduced barrier and to take a shorter path through a hole opened up in a preexisting barrier, respectively. We argue that the ability to solve such problems qualifies the proposed hippocampal object as a cognitive map. Graph theory thus provides a sort of existence proof demonstrating that the hippocampus contains the necessary information to function as a map, in the sense postulated by others (O'Keefe, J., and L. Nadel. 1978. The Hippocampus as a Cognitive Map. Clarendon Press, Oxford, UK). It is also possible that the cognitive mapping functions of the hippocampus are carried out by parallel graph searching algorithms implemented as neural processes. This possibility has the great attraction that the hippocampus could then operate in much the same way to find paths in general problem space; it would only be necessary for pyramidal cells to exhibit a strong nonpositional firing correlate.

Completeness and consistency in hierarchical state-based requirements

Abstract: This paper describes methods for automatically analyzing formal, state-based requirements specifications for some aspects of completeness and consistency. The approach uses a low-level functional formalism, simplifying the analysis process. State-space explosion problems are eliminated by applying the analysis at a high level of abstraction; i.e., instead of generating a reachability graph for analysis, the analysis is performed directly on the model. The method scales up to large systems by decomposing the specification into smaller, analyzable parts and then using functional composition rules to ensure that verified properties hold for the entire specification. The analysis algorithms and tools have been validated on TCAS II, a complex, airborne, collision-avoidance system required on all commercial aircraft with more than 30 passengers that fly in U.S. Airspace.

Optimization-based reconstruction of a 3D object from a single freehand line drawing

Abstract: This paper describes an optimization-based algorithm for reconstructing a 3D model from a single, inaccurate, 2D edge-vertex graph. The graph, which serves as input for the reconstruction process, is obtained from an inaccurate freehand sketch of a 3D wireframe object. Compared with traditional reconstruction methods based on line labelling, the proposed approach is more tolerant of faults in handling both inaccurate vertex positioning and sketches with missing entities. Furthermore, the proposed reconstruction method supports a wide scope of general (manifold and non-manifold) objects containing flat and cylindrical faces. Sketches of wireframe models usually include enough information to reconstruct the complete body. The optimization algorithm is discussed, and examples from a working implementation are given.

Hierarchical partitioning

Abstract: Partitioning of digital circuits has become a key problem area during the last five years. Benefits from new technologies like Multi-Chip-Modules or logic emulation strongly depend on partitioning results. Most published approaches are based on abstract graph models constructed from flat netlists, which consider only connectivity information. The approach presented in this paper uses information on design hierarchy in order to improve partitioning results and reduce problem complexity. Designs up to 150 k gates have been successfully partitioned by descending and ascending the hierarchy. Compared to. Standard k-way iterative improvement partitioning approach results are improved by up to 65% and runtimes are decreased by up to 99%.

Computing Contour Closure

Abstract: Existing methods for grouping edges on the basis of local smoothness measures fail to compute complete contours in natural images: it appears that a stronger global constraint is required. Motivated by growing evidence that the human visual system exploits contour closure for the purposes of perceptual grouping [6, 7, 14, 15, 25], we present an algorithm for computing highly closed bounding contours from images. Unlike previous algorithms [11, 18, 26], no restrictions are placed on the type of structure bounded or its shape. Contours are represented locally by tangent vectors, augmented by image intensity estimates. A Bayesian model is developed for the likelihood that two tangent vectors form contiguous components of the same contour. Based on this model, a sparsely-connected graph is constructed, and the problem of computing closed contours is posed as the computation of shortest-path cycles in this graph. We show that simple tangent cycles can be efficiently computed in natural images containing many local ambiguities, and that these cycles generally correspond to bounding contours in the image. These closure computations can potentially complement region-grouping methods by extending the class of structures segmented to include heterogeneous structures.

A network flow approach to a city emergency evacuation planning

Abstract: Two network flow methods are presented in this paper to optimize a city emergency evacuation plan. The problem is to assign each resident of the city to one of the places of refuge (PR) in preparation for major disasters. We model the city as an undirected graph, and by solving a shortest path problem on this graph, we obtain the shortest evacuation plan. The second model takes the capacity limit on each PR explicitly into account. The problem can then be transformed into a minimal cost flow problem on a slightly modified graph. We can evaluate the efficiency of the current city evacuation plan by comparing this against the optimal solutions of the above stated problems. Also, various pieces of information obtainable from these solutions can be utilized in evaluating the current evacuation policy. In addition, sensitivity analysis can be performed to answer various what-if questions

Topological Algorithms for Digital Image Processing

Abstract: Connected component labelling and adjency graph construction shrinking binary images skeletons of planar patterns parallel connectivity-preserving thinning algorithms on the soundness of surface voxelizations connected, oriented, closed boundaries in digita spaces - theory and algorithms boundaries in digital spaces - basic theory. Appendix: digital topology - a brief introduction and bibliography.

A heuristic estimator for means-ends analysis in planning

Abstract: Means-ends analysis is a seemingly well understood search technique, which can be described, using planning terminology, as: keep adding actions that are feasible and achieve pieces of the goal. Unfortunately, it is often the case that no action is both feasible and relevant in this sense. The traditional answer is to make subgoals out of the preconditions of relevant but infeasible actions. These subgoals become part of the search state. An alternative, surprisingly good, idea is to recompute the entire subgoal hierarchy after every action. This hierarchy is represented by a greedy regression-match graph. The actions near the leaves of this graph are feasible and relevant to a sub...subgoals of the original goal. Furthermore, each subgoal is assigned an estimate of the number of actions required to achieve it. This number can be shown in practice to be a useful heuristic estimator for domains that are otherwise intractable.

Graphical templates for model registration

Abstract: A new method of model registration is proposed using graphical templates. A graph of landmarks is chosen in the template image. All possible candidates for these landmarks are found in the data image using local operators. A dynamic programming algorithm on decomposable subgraphs of the template graph finds the optimal match to a subset of the candidate points in polynomial time. This combination of local operators to describe points of interest/landmarks and a graph to describe their geometric orientation in the plane, yields fast and precise matches of the model to the data, with no initialization required.

Improved algorithms and data structures for solving graph problems in external memory

Abstract: Recently, the study of I/O-efficient algorithms has moved beyond fundamental problems of sorting and permuting and into wider areas such as computational geometry and graph algorithms. With this expansion has come a need for new algorithmic techniques and data structures. In this paper, we present I/O-efficient analogues of well-known data structures that we show to be useful for obtaining simpler and improved algorithms for several graph problems. Our results include improved algorithms for minimum spanning trees, breadth-first search, and single-source shortest paths. The descriptions of these algorithms are greatly simplified by their use of well-defined I/O-efficient data structures with good amortized performance bounds. We expect that I/O efficient data structures such as these will be a useful tool for the design-of I/O-efficient algorithms.

Bayesian model averaging and model selection for markov equivalence classes of acyclic digraphs

Abstract: Acyclic digraphs (ADGs) are widely used to describe dependences among variables in multivariate distributions. In particular, the likelihood functions of ADG models admit convenient recursive factorizations that often allow explicit maximum likelihood estimates and that are well suited to building Bayesian networks for expert systems. There may, however, be many ADGs that determine the same dependence (= Markov) model. Thus, the family of all ADGs with a given set of vertices is naturally partitioned into Markov-equivalence classes, each class being associated with a unique statistical model. Statistical procedures, such as model selection or model averaging, that fail to take into account these equivalence classes, may incur substantial computational or other inefficiencies. Recent results have shown that each Markov-equivalence class is uniquely determined by a single chain graph, the essential graph, that is itself Markov-equivalent simultaneously to all ADGs in the equivalence class. Here we propose t...

Models and tools for quantitative assessment of operational security

Abstract: This paper proposes a novel approach to help computing system administrators in monitoring the security of their systems. The approach is based on modeling the system as a privilege graph exhibiting operational security vulnerabilities and on transforming this privilege graph into a Markov chain corresponding to all possible successful attack scenarios. A set of tools has been developed to support this approach and to provide automatic security evaluation of Unix systems in operation.

Chemical Reaction Networks: A Graph-Theoretical Approach

Abstract: Over the last decade, increased attention to reaction dynamics, combined with the intensive application of computers in chemical studies, mathematical modeling of chemical processes, and mechanistic studies has brought graph theory to the forefront of research. It offers an advanced and powerful formalism for the description of chemical reactions and their intrinsic reaction mechanisms. Chemical Reaction Networks: A Graph-Theoretical Approach elegantly reviews and expands upon graph theory as applied to mechanistic theory, chemical kinetics, and catalysis. The authors explore various graph-theoretical approaches to canonical representation, numbering, and coding of elementary steps and chemical reaction mechanisms, the analysis of their topological structure, the complexity estimation, and classification of reaction mechanisms. They discuss topologically distinctive features of multiroute catalytic and noncatalytic and chain reactions involving metal complexes.With it's careful balance of clear language and mathematical rigor, the presentation of the authors' significant original work, and emphasis on practical applications and examples, Chemical Reaction Networks: A Graph Theoretical Approach is both an outstanding reference and valuable tool for chemical research.

A generic system for form dropout

Abstract: Recent advances in intelligent character recognition are enabling us to address many challenging problems in document image analysis. One of them is intelligent form analysis. This paper describes a generic system for form dropout when the filled-in characters or symbols are either touching or crossing the form frames. We propose a method to separate these characters from form frames whose locations are unknown. Since some of the character strokes are either touching or crossing the form frames, we need to address the following three issues: 1) localization of form frames; 2) separation of characters and form frames; and 3) reconstruction of broken strokes introduced during separation. The form frame is automatically located by finding long straight lines based on the block adjacency graph. Form frame separation and character reconstruction are implemented by means of this graph. The proposed system includes form structure learning and form dropout. First, a form structure-based template is automatically generated from a blank form which includes form frames, preprinted data areas and skew angle. With this form template, our system can then extract both handwritten and machine-typed filled-in data. Experimental results on three different types of forms show the performance of our system. Further, the proposed method is robust to noise and skew that is introduced during scanning.

An Upper Bound on Zarankiewicz' Problem

Abstract: Let ex(n, K3,3) denote the maximum number of edges of a K3,3-free graph on n vertices. Improving earlier results of Kővari, T. Sos and Turan on Zarankiewicz' problem, we obtain that Brown's example for a maximal K3,3-free graph is asymptotically optimal. Hence .

Apparatuses and methods for programming parallel computers

Abstract: A system provides an environment for parallel programming by providing a plurality of modular parallelizable operators stored in a computer readable memory. Each operator defines operation programming for performing an operation, one or more communication ports, each of which is either an input port for providing the operation programming a data stream of records, or an output port for receiving a data stream of records from the operation programming and an indication for each of the operator's input ports, if any, of a partitioning method to be applied to the data stream supplied to the input port. An interface enables users to define a data flow graph by giving instructions to select a specific one of the operators for inclusion in the graph, or instructions to select a specific data object, which is capable of supplying or receiving a data stream of one or more records, for inclusion in the graph, or instructions to associate a data link with a specific communication port of an operator in the graph, which data link defines a path for the communication of a data stream of one or more records between its associated communications port and either a specific data object or the specific communication port of another specific operator in said graph. The execution of a data flow graph equivalent to that defined by the users is automatically parallelized by causing a separate instance of each such operator, including its associated operation programming, to be run on each of multiple processors, with each instance of a given operator having a corresponding input and output port for each input and output port of the given operator, and by automatically partitioning the data stream supplied to the corresponding inputs of the instances of a given operator as a function of the partitioning method indication for the given operator's corresponding input.

Graph partitioning using learning automata

Abstract: Given a graph G, we intend to partition its nodes into two sets of equal size so as to minimize the sum of the cost of the edges having end points in different sets. This problem, called the uniform graph partitioning problem, is known to be NP complete. We propose the first reported learning automaton based solution to the problem. We compare this new solution to various reported schemes such as the B.W. Kernighan and S. Lin's (1970) algorithm, and two excellent recent heuristic methods proposed by E. Rolland et al. (1994; 1992)-an extended local search algorithm and a genetic algorithm. The current automaton based algorithm outperforms all the other schemes. We believe that it is the fastest algorithm reported to date. Additionally, our solution can also be adapted for the GPP in which the edge costs are not constant but random variables whose distributions are unknown.

Multidimensional spectral load balancing

Abstract: A method of and apparatus for graph partitioning involving the use of a plurality of eigenvectors of the Laplacian matrix of the graph of the problem for which load balancing is desired. The invention is particularly useful for optimizing parallel computer processing of a problem and for minimizing total pathway lengths of integrated circuits in the design stage.