563848
An efficient parameterized algorithm for m-set packing
We present an efficient parameterized algorithm solving the Set Packing problem, in which we assume that the size of the sets is bounded by m. In particular, if the size m of the sets is bounded by a constant, then our algorithm is fixed-parameter tractable. For example, if the size of the sets is bounded by 3, then our algorithm runs in time O((5.7k)kn).
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.
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.
39719071
Genomic data modeling
Researchers face many challenges in representing biological data, including: (1) inherent complexity of biological data, (2) domain knowledge barrier, (3) constantly evolving knowledge, and (4) lack of expert data-modeling skills. We have studied how to represent biological sequences and sequence-related genomics concepts using logical data structure. From our multiple experiences in genomic data modeling, we present results in three areas: genomic schema elements, genomic schema fragments, and genomic data modeling lessons. A genomic schema element is a data model that contains only one basic biological sequence notion. Genomic schema elements provide biology data modelers with baseline thoughts in genomic data modeling. A genomic schema fragment is a data model that contains only one genomic topic area. Genomic schema fragments provide biology data modelers with successful design solutions that they can adapt to fit their own problem's needs. Genomic data modeling lessons address issues particularly important to genomic data modeling such as modeling contextual information, modeling intermediate and derived data, modeling inconsistent data, and modeling categorical rules. Genomic data modeling lessons provide novice biology data modelers with enriched principles from content-neutral data modeling techniques. In all, we have demonstrated how to manage evolving genomic knowledge concepts and discovery results using data modeling techniques extended into the genomics domain.
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.
12151643
Discretization Approach and Nonparametric Modeling for Long-Term HIV Dynamic Model
Modeling viral load response in long-term HIV dynamics is important for AIDS clinical study. It allows one to examine how a patient recuperates for an antiviral treatment. This paper investigates a discretization approach to the viral load based on a long-term HIV dynamic model. We propose a two-stage nonparametric procedure for estimating the viral load and the time-varying new productive virus. Simulation study shows that the proposed estimated methods are efficient and powerful for fitting long-term viral load measurements.
8059419
Asymptotic analysis of MIMO wireless systems with spatial correlation at the receiver
With a unified approach, this paper investigates the asymptotic performance or, equivalently, the large-system properties, of various point-to-point systems with antenna-array-based multiple-input multiple-output (MIMO) channels having spatial correlations. Using the replica method originally developed for statistical physics, we provide analytical solutions to the input-output mutual information of MIMO systems: 1) at the transmit side, with arbitrary inputs, and 2) at the receive side, with either the optimum space-time joint decoding or various suboptimum spatial equalizers followed by a bank of temporal decoders. Important physical meanings revealed though the analytical solutions to those more practical combinations, such as how the input-output mutual information is affected by the channel spatial correlations, are highlighted along our derivation. Moreover, we provide a novel waterfilling algorithm to determine the data-rate-maximizing transmit signal covariance matrix when only the channel long-term spatial correlations are available at the transmitter.
8668982
Perceptually-tuned multiscale color-texture segmentation
We present a perceptually-tuned multiscale image segmentation algorithm that is based on spatially adaptive color and texture features. The proposed algorithm extends a previously proposed approach to include multiple texture scales. The determination of the multiscale texture features is based on perceptual considerations. We also examine the perceptual tuning of the algorithm and how it is affected by the presence of different texture scales. The multiscale extension is necessary for segmenting higher resolution images and is particularly effective in segmenting objects shown in different perspectives. The performance of the proposed algorithm is demonstrated in the domain of photographic images.