16597098
Regular meshes
This paper presents our preliminary results on regular meshes in which all faces have the same size and all vertices have the same valence. A regular mesh is denoted by (<i>n, m, g</i>) where <i>n</i> is the number of the sides of faces, <i>m</i> is the valence of vertices and <i>g</i> is the genus of the mesh. For <i>g</i> = 0, regular meshes include regular platonic solids, all two sided polygons. For <i>g</i> = 1 regular meshes include regular tilings of infinite plane. Our work shows that there exist infinitely many regular meshes for <i>g</i> > 1. Moreover, we have constructive proofs that describe how to create high genus regular meshes that consist of triangles and quadrilaterals (3, <i>m</i>, <i>g</i>) and (4, <i>m</i>, <i>g</i>).
5242879
Interactive rind modeling
In this paper, we describe a technique, with roots in topological graph theory, that we call rind modeling. It provides for the easy creation of surfaces resembling peeled and punctured rinds. We show how the method's two main steps of: 1) creation of a shell or crust like the rind of an orange, and 2) opening holes in the crust by punching or peeling can be encapsulated into a real time semi-automatic interactive algorithm. We include a number of worked examples, some by students in a first modeling course, that demonstrate the ease with which a large variety of intricate rind shapes can be created.
3146463
On Strong Menger-Connectivity of Star Graphs
Motivated by parallel routing in networks with faults, we study the following graph theoretical problem. Let G be a d-regular graph. We say that G is strongly Menger-connected if for any copy Gf of G with at most d - 2 nodes removed, every pair of nodes u and v in Gf are connected by min{deg f(u), deg f(v)} node-disjoint paths in Gf, where deg f(u) and deg f(v) are the degrees of the nodes u and v in Gf, respectively. We show that the star graphs, which are a recently proposed attractive alternative to the widely used hypercubes as network models, are strongly Menger-connected. An algorithm of optimal running time is developed that constructs the maximum number of node-disjoint paths of nearly optimal length in star graphs with faults.
1021255
A minimal and complete set of operators for the development of robust manifold mesh modelers
In this paper, we identify a minimal and complete set of fundamental operators, which is necessary and sufficient for performing all homeomorphic and topological operations on 2- manifold mesh structures. Efficient algorithms are developed for the implementation of these operators. We also developed a set of powerful, user-friendly, and effective operators at the level of user-interface. Using these operators, we have developed a prototype system for robust, interactive, and user-friendly modeling of orientable 2-manifold meshes. Users of our system can perform a large set of homeomorphic and topological changes with these user-interface level operators. Our system is topologically robust in the sense that users will never create invalid 2-manifold mesh structure with these operators. In our system, the homeomorphic and topological surgery operations can be applied alternatively on 2-manifold meshes. With our system, users can blend surfaces, construct rinds, and open holes on these rind shapes. With our system, the shapes that look like solid, non-manifold, or 2-manifold with boundary can be manipulated. The system also provides automatic texture mapping during topology changes.
2261180
Graph Ear Decompositions and Graph Embeddings
Ear decomposition of a graph has been extensively studied in relation to graph connectivity. In this paper, a connection of ear decomposition to graph embeddings is exhibited. It is shown that constructing a maximum-paired ear decomposition of a graph and constructing a maximum-genus embedding of the graph are polynomial-time equivalent. Applications of this connection are discussed.
16331940
Optimal Parallel Routing in Star Networks
Star networks have recently been proposed as attractive alternatives to the popular hypercube for interconnecting processors on a parallel computer. In this paper, we present an efficient algorithm that constructs an optimal parallel routing in star networks. Our result improves previous results for the problem.
9144862
Rules and fuzzy rules in text: concept, extraction and usage
Several concepts and techniques have been imported from other disciplines such as Machine Learning and Artificial Intelligence to the field of textual data. In this paper, we focus on the concept of rule and the management of uncertainty in text applications. The different structures considered for the construction of the rules, the extraction of the knowledge base and the applications and usage of these rules are detailed. We include a review of the most relevant works of the different types of rules based on their representation and their application to most of the common tasks of Information Retrieval such as categorization, indexing and classification.
7457791
Choosing Among Alternative Futures
Non-determinism is a serious impediment to testing and debugging concurrent programs. Such programs do not execute the same way each time they are run, which can hide the presence of errors. Existing techniques use a variety of mechanisms that attempt to increase the probability of uncovering error conditions by altering the execution sequence of a concurrent program, but do not test for specific errors. This paper presents some preliminary work in deterministically executing a multithreaded program using a combination of an intermediate compiler form that identifies the set of writes of a shared variable by other threads are visible at a given read of that variable and aspect-oriented programming to control program execution. Specifically, the aspects allow a read of a shared variable to return any of the reaching definitions, where the desired definition can be selected before the program is run. As a result, we can deterministically run test cases. This work is preliminary and many issues have yet to be resolved, but we believe this idea shows some promise.
39815337
Making Timed Automata Communicate
A computation model is introduced in which real-time constraints as well as data communications can be explicitely expressed. The model is presented in a graphical form. Its semantics is studied and algorithms to compute bisimulation equivalences for such graphs are proposed.
36905463
Quasi-threshold Graphs
Abstract Quasi-threshold graphs are defined recursively by the following rules: 1. (1) K1 is a quasi-threshold graph, 2. (2) adding a new vertex adjacent to all vertices of a quasi-threshold graph results in a quasi-threshold graph, 3. (3) the disjoint union of two quasi-threshold graphs is a quasi-threshold graph. This paper gives some new equivalent definitions of a quasi-threshold graph. From them, linear time recognition algorithms follow. We also give linear time algorithms for the edge domination problem and the bandwidth problem in this class of graphs.
26236484
A new object-oriented method integrating Jackson structured programming method
Abstract This article presents a new object-oriented method which integrates the Jackson Structured Programming method with an object-oriented approach. The new method analyzes the user's services, identifies attributes from data structure diagrams, and identifies operations from program structure diagrams. Also, this method defers the identification of class relationships until the attributes and operations have been identified, so as to prevent premature decisions. In addition, the concept of “leading object” is used to decrease the number of actors and agents and to increase the number of servers in a system. This may enhance reusability of the objects.