1481165
Improved algorithms for path, matching, and packing problems
Improved randomized and deterministic algorithms are presented for PATH, MATCHING, and PACKING problems. Our randomized algorithms are based on the divide-and-conquer technique, and improve previous best algorithms for these problems. For example, for the <i>k</i>-PATH problem, our randomized algorithm runs in time <i>O</i>(4<sup><i>k</i></sup>k<sup>3.42</sup><i>m</i>) and space <i>O</i>(<i>nk</i>log<i>k</i> + <i>m</i>), improving the previous best randomized algorithm for the problem that runs in time <i>O</i>(5.44<sup><i>k</i></sup>km) and space <i>O</i>(2<sup><i>k</i></sup>kn + <i>m</i>). To achieve improved deterministic algorithms, we study a number of previously proposed de-randomization schemes, and also develop a new derandomization scheme. These studies result in a number of deterministic algorithms: one of time <i>O</i>(4<sup><i>k</i>+<i>o(k)</i></sup>m) for the <i>k</i>-PATH problem, one of time <i>O</i>(2.80<sup>3<i>k</i></sup>k nlog<sup>2</sup> <i>n</i>) for the 3-D MATCHING problem, and one of time <i>O</i>(4<sup>3<i>k</i>+<i>o(k)</i></sup>n) for the 3-SET PACKING problem. All these significantly improve previous best algorithms for the 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.
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.
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.
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.
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.
16592812
A web-based virtual laboratory on a frequency modulation experiment
With the rapid proliferation of Internet technologies, accessing and operating engineering instruments remotely anytime anywhere is fast becoming a reality. This paper presents a new Web-based virtual laboratory on a frequency modulation experiment for the teaching of an undergraduate course on communication principles in the National University of Singapore (NUS). The laboratory requires only a common Web browser to access and incorporate schemes for reducing data traffic and authenticating users. It enables students to have a natural hands-on experience of using an expensive spectrum analyzer on a one-to-one basis and provides a solution for distant engineering education. The system uses a double client-server structure where access to the experiment is via two rounds of client-server processing. The virtual laboratory can be accessed at the Web site http://vlab.ee.nus.edu.sg/vlab/freqmod/index.html.
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.
46388294
Soft Sorting in Logic Programming
Integrating sorts (types) into logic programming languages increases their expressiveness and evaluation efficiency. The sort structures usually considered are strict, in the sense that whenever an expression has a subexpression which is not properly sorted, the expression is classified as ill-sorted, and in effect is regarded as meaningless. Typically a logic programming language with strict sorting is incomplete, in the sense that some intuitively meaningful programs and queries are ill-sorted and hence are not part of the language.
29466407
An adaptive transmission scheme for audio and video synchronization based on real-time transport protocol
Multimedia streams impose tight temporal constraints since different kinds of continuous multimedia streams have to be played synchronously. We devise in this paper an adaptive transmission scheme to ensure the continuous and synchronous playback of audio and video streams based on Real-time Transport Protocol. Realization of our adaptive scheme is composed of a series of operations in three stages, namely, (1) dynamic reordering mechanism, (2) decoding-recovery mechanism, and (3) adaptive synchronization mechanism. An empirical study is conducted to provide insights into our adaptive transmission scheme. As validated by our simulation results, the adaptive transmission mechanism is able to strike a good balance of both stable playback and the end-to-end delay reduction. Furthermore, we analyze the jitter resistance, the end-to-end delay, and the buffer size required in order to enhance the applicability of this scheme to more applications that require the transmission of multimedia data.