44298104
Tight Lower Bounds for Certain Parameterized NP-Hard Problems
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.
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.
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.
31382426
Strong Fault-Tolerance: Parallel Routing in Networks with Faults
A d-regular network G is strongly fault-tolerant if for any copy Gf of G with at most d - 2 faulty nodes, every pair of nonfaulty nodes u and v in Gf admits min{df(u), df (v)} node-disjoint paths in Gf from u to v, where df(u) and df(v) are the degrees of the nodes u and v in Gf. We show that popular network structures, such as hypercube and star networks, are strongly fault-tolerant. We develop efficient algorithms that construct the maximum number of node-disjoint paths of optimal or nearly optimal length in these networks with faulty nodes. Our algorithms are optimal in terms of their running time.
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.
42532593
A Sound and Complete Fuzzy Logic System Using Zadeh's Implication Operator
We present a formalization of fuzzy logic based on Zadeh's implication operator a→b=max{1-a, b}. Our logical system allows the specification of both lower and upper bounds of the truth value of a formula. We present a specific system of axioms and inference rules which are both sound and complete. We also provide a generalization of the classical resolution method which acts as a decision procedure in a finite fuzzy theory.
30548729
A Class of Stratified Programs in Autoepistemic Logic of Knowledge and Belief
Przymusinski proposed [11] AELB, the autoepistemic logic of knowledge and belief. The AELB logic is a very powerful and expressive formal system which isomorphically contains various major non-monotonic knowledge representation formalisms and major logic program semantics. Thus AELB can be used as a unifying framework for non-monotonic knowledge representation formalisms, which allows us to compare and better understand different formalizations of common-sense knowledge.
33412733
Learning a Hidden Graph Using O(log n) Queries Per Edge
We consider the problem of learning a general graph using edge-detecting queries. In this model, the learner may query whether a set of vertices induces an edge of the hidden graph. This model has been studied for particular classes of graphs by Kucherov and Grebinski [1] and Alon et al.[2], motivated by problems arising in genome sequencing. We give an adaptive deterministic algorithm that learns a general graph with n vertices and m edges using O(m log n) queries, which is tight up to a constant factor for classes of non-dense graphs. Allowing randomness, we give a 5-round Las Vegas algorithm using \(O(m {\rm log}n+\sqrt{m}{\rm log}^{2}n)\) queries in expectation. We give a lower bound of Ω((2m/r) r/2) for learning the class of non-uniform hypergraphs of dimension r with m edges. For the class of r-uniform hypergraphs with bounded degree d, where d≤ n 1/( r− − 1)/(2r 1 + 2/( r− − 1)), we give a non-adaptive Monte Carlo algorithm using O(dnlog n) queries, which succeeds with probability at least 1–n − − c, where c is any constant.
36321582
Enacting object-oriented methods by a process environment
Abstract This paper describes modeling and enactment of two object-oriented methods, namely the OMT method and the Booch method, using the concurrent software process language (CSPL). CSPL is a process-centered environment using Ada95-like syntax to model a method as a process program which is then compiled to C-shell executing in UNIX. A method can thus be enacted (executed) using this approach. Experiences of the approach are depicted. It is demonstrated that CSPL is feasible and appropriate for modeling and enacting methods, including object-oriented methods. Additionally, partial CSPL program modeling the Booch method is included in the Appendix.
31224210
The strong semantics for logic programs
Recently, the well-founded semantics of a logic programP has been strengthened to the well-founded semantics-by-case (WFC) and this in turn has been strengthened to the extended well-founded semantics (WFE). Both WFC(P) and WFE(P) have thelogical consequence property, namely, if an atomAj is true in the theory Th(P), thenAj is true in the semantics as well. However, neither WFC nor WFE has the GCWA property, i.e., if an atomAj is false in all minimal models ofP,Aj may not be false in WFC(P) (resp. WFE(P)). We extend the ideas in WFC and WFE to define a strong well-founded semantics WFS which has the GCWA property. The strong semantics WFS(P) is defined by combining GCWA with the notion ofderived rules. Here we use a new Type-III derived rules in addition to those used in WFC and WFE. The relationship between WFS and WFC is also clarified.