18066023
Improvement on vertex cover for low-degree graphs
The Vertex Cover problem (given a graph G and an integer k, decide if G has a vertex cover of k vertices) is one of the six “basic” NP-complete problems according to Garey and Johnson [7]. It is fixed-parameter tractable in terms of Downey and Fellows [5], that is, it can be solved in time O(f(k)n), where f is a function of the parameter k but independent of the input length n and c is a constant independent of the parameter k. Continuous efforts have been made in improving fixed-parameter tractable algorithms for the vertex cover problem, starting from Buss’ algorithm of running time O(kn + 2kk2k+2) [2]. Downey and Fellows [4] developed an O(kn + 2kk2) time algorithm. More recently, Balasubramanian et al. [1] developed an O(kn+1.3247kk2) time algorithm. Later Downey et al. [6] improved the result slightly to time complexity O(kn + 1.3195kk2), and Niedermeier and Rossmanith [9] developed an algorithm of time O(kn+1.2918kk2). More recently, Chen et al. [3] developed an O(kn + 1.271kk2) time algorithm. For the restricted version of the vertex
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.
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.
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.
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.
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.
19801796
Multimedia Over IP For Thin Clients : Building A Collaborative Resource-Sharing Prototype
This paper describes the issues and the techniques of enabling multimedia applications with thin-client/server computing. A prototype of a video communication system based on H.323 family of ITU-T recommendations has been developed to demonstrate the efficient support to multimedia applications with a terminal server and thin clients in an IP-based thin-client computing environment. With the proposed architecture, a collaborative multi-user audio/video conference system is presented as an illustrative application. The collaborative multiuser audio/video conference system leverages the benefit of sharing common components among multiple conference terminals as well as increases their extensibility and ease of use. As a result, we can attain a balanced architecture that supports both centralized management of application softwares and distributed multimedia processing for I/O devices.
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.
852665
Location-based scheduling and pricing for energy and reserves: a responsive reserve market proposal
It is well known that given a network that can become constrained on voltage or real power flows, reserves must also be spatially located in order to handle all credible contingencies. However, to date, there is no credible science-based method for assigning and pricing reserves in this way. Presented in this paper is a responsive-reserve scheduling algorithm incorporating constraints imposed by grid security considerations, which include one base case (intact system) and a list of credible contingencies (line out, unit lost, and load growth) of the system. By following a cost-minimizing co-optimization procedure, both power and reserves are allocated spatially for the combined energy and reserve markets. With the Lagrange multipliers obtained, the scheduling algorithm also reveals the locational shadow prices for the reserve and energy requirements. Unlike other pricing and scheduling methods in use, which are usually ad hoc and are based on engineering judgment and experience, this proposed formulation is likely to perform better in restructured markets when market power is a potential problem. An illustrative example of a modified IEEE 30-bus system is used to introduce concepts and present results.
6192242
Computing Maximum-Scoring Segments in Almost Linear Time
Given a sequence, the problem studied in this paper is to find a set of k disjoint continuous subsequences such that the total sum of all elements in the set is maximized. This problem arises naturally in the analysis of DNA sequences. The previous best known algorithm requires Θ(n log n) time in the worst case. For a given sequence of length n, we present an almost linear-time algorithm for this problem. Our algorithm uses a disjoint-set data structure and requires O(nα(n, n)) time in the worst case, where α(n, n) is the inverse Ackermann function.
15909369
New Models for Improving Supertag Disambiguation
In previous work, supertag disambiguation has been presented as a robust partial parsing technique. In this paper we present two approaches: contextual models, which exploit a variety of features in order to improve supertag performance, and class-based models, which assign sets of supertags to words in order to substantially improve accuracy with only a slight increase in ambiguity.