2863452
Optimal Polygon Cover Problems and Applications
Polygon cover problems are important in several applied areas, such as material layout, layered manufacturing, radiation therapy and radiosurgery, etc. In this paper, we study three optimal polygon cover problems: monotone polygon cover among obstacles, star-shaped polygon cover among obstacles, and strip cover for trapezoidalized polygons. Based on some interesting geometric observations, we develop efficient algorithms for solving these problems. The complexity bounds of our monotone cover and star-shaped cover algorithms are comparable to those of the previously best known algorithms for simpler cases of the problems without considering obstacles. Our strip cover algorithm improves the quality of the previously best known solutions.
6260724
Finding an optimal path without growing the tree
For problems on computing an optimal path as well as its length in a certain setting, the "standard" approach for finding an actual optimal path is by building (or "growing") a single-source optimal path tree. In this paper, we study a class of optimal path problems with the following phenomenon: The space complexity of the algorithms for reporting the lengths of single-source optimal paths for these problems is asymptotically smaller than the space complexity of the "standard" tree-growing algorithms for finding actual optimal paths. We present a general and efficient algorithmic paradigm for finding an actual optimal path for such problems without having to grow a single-source optimal path tree. Our paradigm is based on the "marriage-before-conquer" strategy, the prune-and-search technique, and a new data structure called clipped trees. The paradigm enables us to compute an actual path for a number of optimal path problems and dynamic programming problems in computational geometry, graph theory, and combinatorial optimization. Our algorithmic solutions improve the space bounds (in certain cases, the time bounds as well) of the previously best known algorithms, and settle some open problems. Our techniques are likely to be applicable to other problems.
16662300
A comparative investigation on subspace dimension determination
It is well-known that constrained Hebbian self-organization on multiple linear neural units leads to the same k-dimensional subspace spanned by the first k principal components. Not only the batch PCA algorithm has been widely applied in various fields since 1930s, but also a variety of adaptive algorithms have been proposed in the past two decades. However, most studies assume a known dimension k or determine it heuristically, though there exist a number of model selection criteria in the literature of statistics. Recently, criteria have also been obtained under the framework of Bayesian Ying-Yang (BYY) harmony learning. This paper further investigates the BYY criteria in comparison with existing typical criteria, including Akaike's information criterion (AIC), the consistent Akaike's information criterion (CAIC), the Bayesian inference criterion (BIC), and the cross-validation (CV) criterion. This comparative study is made via experiments not only on simulated data sets of different sample sizes, noise variances, data space dimensions, and subspace dimensions, but also on two real data sets from air pollution problem and sport track records, respectively. Experiments have shown that BIC outperforms AIC, CAIC, and CV while the BYY criteria are either comparable with or better than BIC. Therefore, BYY harmony learning is a more preferred tool for subspace dimension determination by further considering that the appropriate subspace dimension k can be automatically determined during implementing BYY harmony learning for the principal subspace while the selection of subspace dimension k by BIC, AIC, CAIC, and CV has to be made at the second stage based on a set of candidate subspaces with different dimensions which have to be obtained at the first stage of learning.
6833692
Clustering Large Collection of Biomedical Literature Based on Ontology-Enriched Bipartite Graph Representation and Mutual Refinement Strategy
In this paper we introduce a novel document clustering approach that solves some major problems of traditional document clustering approaches. Instead of depending on traditional vector space model, this approach represents a set of documents as bipartite graphs using domain knowledge in ontology. In this representation, the concepts of the documents are classified according to their relationships with documents that are reflected on the bipartite graph. Using the concept groups, documents are clustered based on the concepts' contribution to each document. Through the mutual-refinement relationship with concept groups and document groups, the two groups are recursively refined. Our experimental results on MEDLINE articles show that our approach outperforms two leading document clustering algorithms: BiSecting K-means and CLUTO. In addition to its decent performance, our approach provides a meaningful explanation for each document cluster by identifying its most contributing concepts, thus helps users to understand and interpret documents and clustering results.
2425436
Cluster Ensemble and Its Applications in Gene Expression Analysis
Huge amount of gene expression data have been generated as a result of the human genomic project. Clustering has been used extensively in mining these gene expression data to find important genetic and biological information. Obtaining high quality clustering results is very challenging because of the inconsistency of the results of different clustering algorithms and noise in the gene expression data. Many clustering algorithms are available and different clustering algorithms may generate different clustering results due to their bias and assumptions. It is a challenging and daunting task for the genomic researchers to choose the best clustering algorithm and generate the best clustering results for their data sets. In this paper, we present a cluster ensemble framework for gene expression analysis to generate high quality and robust clustering results. In our framework, the clustering results of individual clustering algorithm are converted into a distance matrix, these distance matrices are combined and a weighted graph is constructed according to the combined matrix. Then a graph partitioning approach is used to cluster the graph to generate the final clusters. The experiment results indicate that cluster ensemble approach yields better clustering results than the single best clustering algorithm on both synthetic data set and yeast gene expression data set.
10166803
An-OARSMan: obstacle-avoiding routing tree construction with good length performance
Routing is one of the important steps in VLSI/ULSI physical design. The rectilinear Steiner minimum tree (RSMT) construction is an essential part of routing. Since macro cells, IP blocks, and pre-routed nets are often regarded as obstacles in the routing phase, obstacle-avoiding RSMT (OARSMT) algorithms are useful for practical routing applications. This paper focuses on the OARSMT problem and presents an algorithm, named An-OARSMan, based on ant colony optimization. A greedy obstacle penalty distance (OP-distance) local heuristic is used in the algorithm and performed on the track graph. The algorithm has been implemented and tested on different kinds of obstacles. Experimental results show that An-OARSMan can handle complex obstacle cases including both convex and concave polygon obstacles with good length performance. It can always achieve the optimal solution in the cases with no more than 7 terminals.
40136335
On Rearrangeability of Multirate Clos Networks
Chung and Ross [SIAM J. Comput., 20 (1991), pp. 726--736] conjectured that the multirate three-stage Clos network C(n,2n-1,r) is rearrangeable in the general discrete bandwidth case; i.e., each connection has a weight chosen from a given finite set {p1, p2,. . .,pk} where $1 \geq p_1 > p_2 > \cdots > p_k > 0$ and pi is an integer multiple of pi, denoted by $p_k \mid p_i$, for $1 \leq i \leq k-1$. In this paper, we prove that multirate three-stage Clos network C(n,2n-1,r) is rearrangeable when each connection has a weight chosen from a given finite set {p1, p2,. . .,pk} where $1 \geq p_1 > p_2 > \cdots > p_{h} > 1/2 \geq p_{h+1} > \cdots > p_k > 0$ and ph+2 | ph+1,ph+3 |ph+2,. . . ,pk | ph+1. We also prove that C(n,2n-1,r) is two-rate rearrangeable and $C(n, \lceil \frac{7n}{3} \rceil, r)$ is three-rate rearrangeable.