20682205
Greedy Localization and Color-Coding: Improved Matching and Packing Algorithms
Matching and packing problems have formed an important class of NP-hard problems. There have been a number of recently developed techniques for parameterized algorithms for these problems, including greedy localization, color-coding plus dynamic programming, and randomized divide-and-conquer. In this paper, we provide further theoretical study on the structures of these problems, and develop improved algorithmic methods that combine existing and new techniques to obtain improved algorithms for matching and packing problems. For the 3-SET PACKING problem, we present a deterministic algorithm of time O*(4.613 k ), which significantly improves the previous best deterministic algorithm of time O* (12.8 3k For the 3-D MATCHING problem, we develop a new randomized algorithm of running time O*(2.32 3k ) and a new deterministic algorithm of running time O* (2.77 3k ). Our randomized algorithm improves the previous best randomized algorithm of running time O*(2.52 3k ), and our deterministic algorithm significantly improves the previous best deterministic algorithm of running time O* (12.8 3k ). Our results also imply improved algorithms for various triangle packing problems in graphs.
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.
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.
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.
34159049
Approximation algorithms for scheduling real-time jobs with multiple feasible intervals
Time-critical jobs in many real-time applications have multiple feasible intervals. Such a job is constrained to execute from start to completion in one of its feasible intervals. A job fails if the job remains incomplete at the end of the last feasible interval. Earlier works developed an optimal off-line algorithm to schedule all the jobs in a given job set and on-line heuristics to schedule the jobs in a best effort manner. This paper is concerned with how to find a schedule in which the number of jobs completed in one of their feasible intervals is maximized. We show that the maximization problem is $${\cal N}{\cal P}$$-hard for both non-preemptible and preemptible jobs. This paper develops two approximation algorithms for non-preemptible and preemptible jobs. When jobs are non-preemptible, Algorithm Least Earliest Completion Time First (LECF) is shown to have a 2-approximation factor; when jobs are preemptible, Algorithm Least Execution Time First (LEF) is proved being a 3-approximation algorithm. We show that our analysis for the two algorithms are tight. We also evaluate our algorithms by extensive simulations. Simulation results show that Algorithms LECF and LEF not only guarantee the approximation factors but also outperform other multiple feasible interval scheduling algorithms in average.
36997041
The Logic of Only Knowing as a Unified Framework for Non-Monotonic Reasoning
We propose to use the logic of only knowing (OL) by Levesque [10] as a unified framework that encompasses various non-monotonic formalisms and logic programming. OL is a modal logic which can be used to formalize an agent's introspective reasoning and to answer epistemic queries to databases. The OL logic allows one to formally express the statement “α is all I know” (in symbols, Oα) and to perform inferencing based on only-knowing, which is very useful for commonsense reasoning. Another nice thing about the OL logic is that it has a clear model-theoretic semantics and a simple proof theory, which is sound for the quantificational case, and both sound and complete for the prepositional case. We establish the relations between OL and various non-monotonic logics (such as default logic, circumscription) and logic programming, thus extending the existing works relating the OL logic with other non-monotonic reasoning formalisms (e.g., Levesque showed that autoepistemic logic can be embeded in OL). This is accomplished by finding the connection between OL and MBNF, the logic of Minimal Belief and Negation as Failure proposed by Lifschitz [12, 13], which is known to have close relationship with logic programming and other non-monotonic logics. Our results show that OL can be used as a unified framework to compare different non-monotonic formalisms based on the same domain.
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.
6316461
Partitioned optimization algorithms for multiple sequence alignment
Multiple sequence alignment is an important and difficult problem in molecular biology and bioinformatics. In this paper, we propose a partitioning approach that significantly improves the solution time and quality by utilizing the locality structure of the problem. The algorithm solves the multiple sequence alignment in three stages. First, an automated and suboptimal partitioning strategy is used to divide the set of sequences into several subsections. Then a multiple sequence alignment algorithm based on ant colony optimization is used to align the sequences of each subsection. Finally, the alignment of original sequences can be obtained by assembling the result of each subsection. The ant colony algorithm is highly optimized in order to avoid local optimal traps and converge to global optimal efficiently. Experimental results show that the algorithm can significantly reduce the running time and improve the solution quality on large-scale multiple sequence alignment benchmarks.
119479
Visualizing and discovering web navigational patterns
Web site structures are complex to analyze. Cross-referencing the web structure with navigational behaviour adds to the complexity of the analysis. However, this convoluted analysis is necessary to discover useful patterns and understand the navigational behaviour of web site visitors, whether to improve web site structures, provide intelligent on-line tools or offer support to human decision makers. Moreover, interactive investigation of web access logs is often desired since it allows ad hoc discovery and examination of patterns not a priori known. Various visualization tools have been provided for this task but they often lack the functionality to conveniently generate new patterns. In this paper we propose a visualization tool to visualize web graphs, representations of web structure overlaid with information and pattern tiers. We also propose a web graph algebra to manipulate and combine web graphs and their layers in order to discover new patterns in an ad hoc manner.