Curve-skeleton properties, applications, and algorithms

Curve-skeletons are thinned 1D representations of 3D objects useful for many visualization tasks including virtual navigation, reduced-model formulation, visualization improvement, animation, etc. There are many algorithms in the literature describing extraction methodologies for different applications; however, it is unclear how general and robust they are. In this paper, we provide an overview of many curve-skeleton applications and compile a set of desired properties of such representations. We also give a taxonomy of methods and analyze the advantages and drawbacks of each class of algorithms     

Fast and scalable selection algorithms with applications to median filtering

The main contributions of this paper are in designing fast and scalable parallel algorithms for selection and median filtering. Based on the radix-/spl omega/ representation of data and the prune-and-search approach, we first design a fast and scalable selection algorithm on the arrays with reconfigurable optical buses (AROB). To the authors' knowledge, this is the most time efficient algorithm yet published, especially compared to the algorithms proposed by Han et al (2002) and Pan (1994). Then, given an N /spl times/ N image and a W /spl times/ W window, based on the proposed selection algorithm, several scalable median filtering algorithms are developed on the AROB model with a various number of processors. In the sense of the product of time and the number of processors used, most of the proposed algorithms are time or cost optimal.     

Cyclic routing algorithms in graphs: Performance analysis and applications to robot scheduling

In this paper we revisit and extend the algorithm for the cyclic project scheduling problem which was originally proposed by Romanovskii (1967). While the algorithm has been derived for fixed numerical data, we show how it can be extended to handle the problems with interval data. We also propose a new algorithm for the cyclic scheduling problem with interval data that extends the parametric method developed by Megiddo (1979) and runs in strongly polynomial time.     

Computing median and antimedian sets in median graphs

The median (antimedian) set of a profile π=(u ₁,…,u _k ) of vertices of a graph G is the set of vertices x that minimize (maximize) the remoteness ∑ _i d(x,u _i ). Two algorithms for median graphs G of complexity O(n idim(G)) are designed, where n is the order and idim(G) the isometric dimension of G. The first algorithm computes median sets of profiles and will be in practice often faster than the other algorithm which in addition computes antimedian sets and remoteness functions and works in all partial cubes.     

Graphlet decomposition: framework,algorithms, and applications

From social science to biology, numerous applications often rely on graphlets for intuitive and meaningful characterization of networks. While graphlets have witnessed a tremendous success and impact in a variety of domains, there has yet to be a fast and efficient framework for computing the frequencies of these subgraph patterns. However, existing methods are not scalable to large networks with billions of nodes and edges. In this paper, we propose a fast, efficient, and parallel framework as well as a family of algorithms for counting k-node graphlets. The proposed framework leverages a number of theoretical combinatorial arguments that allow us to obtain significant improvement on the scalability of graphlet counting. For each edge, we count a few graphlets and obtain the exact counts of others in constant time using the combinatorial arguments. On a large collection of \(300+\) networks from a variety of domains, our graphlet counting strategies are on average \(460{\times }\) faster than existing methods. This brings new opportunities to investigate the use of graphlets on much larger networks and newer applications as we show in the experiments. To the best of our knowledge, this paper provides the largest graphlet computations to date.     

Toeplitz matrices: Structures,algorithms and applications

This volume contains papers presented at the workshop “Toeplitz Matrices: Structures, Algorithms and Applications”. The workshop was held in Cortona, Italy, from 9 through 12 September 1996.     

Distance-based outliers: algorithms and applications

This paper deals with finding outliers (exceptions) in large, multidimensional datasets. The identification of outliers can lead to the discovery of truly unexpected knowledge in areas such as electronic commerce, credit card fraud, and even the analysis of performance statistics of professional athletes. Existing methods that we have seen for finding outliers can only deal efficiently with two dimensions/attributes of a dataset. In this paper, we study the notion of DB (distance-based) outliers. Specifically, we show that (i) outlier detection can be done efficiently for large datasets, and for k-dimensional datasets with large values of k (e.g., ); and (ii), outlier detection is a meaningful and important knowledge discovery task. First, we present two simple algorithms, both having a complexity of , k being the dimensionality and N being the number of objects in the dataset. These algorithms readily support datasets with many more than two attributes. Second, we present an optimized cell-based algorithm that has a complexity that is linear with respect to N, but exponential with respect to k. We provide experimental results indicating that this algorithm significantly outperforms the two simple algorithms for . Third, for datasets that are mainly disk-resident, we present another version of the cell-based algorithm that guarantees at most three passes over a dataset. Again, experimental results show that this algorithm is by far the best for . Finally, we discuss our work on three real-life applications, including one on spatio-temporal data (e.g., a video surveillance application), in order to confirm the relevance and broad applicability of DB outliers. Received February 15, 1999 / Accepted August 1, 1999     

The image foresting transform: theory, algorithms, and applications

The image foresting transform (IFT) is a graph-based approach to the design of image processing operators based on connectivity. It naturally leads to correct and efficient implementations and to a better understanding of how different operators relate to each other. We give here a precise definition of the IFT, and a procedure to compute it-a generalization of Dijkstra's algorithm-with a proof of correctness. We also discuss implementation issues and illustrate the use of the IFT in a few applications.     

Deduction graphs: an algorithm and applications

A deduction graph (DG) for logically deducing a new functional dependency (FD) or function-free Horn formula (extended from Horn clauses) from a subset of a given FDs or function-free headed Horn clauses in a relational database or rule-based expert systems is defined. An algorithm with a polynomial time complexity for constructing a DG based on a number of rules is designed. Applications of DGs to relational databases, rule-based expert systems, logic programming, and artificial intelligence are investigated. In addition to graphically solving the inference problem by DGs, many logic queries can be answered by DGs with substitutions for unifying expressions     

Tree spanners on chordal graphs: complexity and algorithms

A tree t-spanner T in a graph G is a spanning tree of G such that the distance in T between every pair of vertices is at most t times their distance in G. The T t-S problem asks whether a graph admits a tree t-spanner, given t. We substantially strengthen the hardness result of Cai and Corneil (SIAM J. Discrete Math. 8 (1995) 359–387) by showing that, for any t4, T t-S is NP-complete even on chordal graphs of diameter at most t+1 (if t is even), respectively, at most t+2 (if t is odd). Then we point out that every chordal graph of diameter at most t−1 (respectively, t−2) admits a tree t-spanner whenever t2 is even (respectively, t3 is odd), and such a tree spanner can be constructed in linear time.

The complexity status of T 3-S still remains open for chordal graphs, even on the subclass of undirected path graphs that are strongly chordal as well. For other important subclasses of chordal graphs, such as very strongly chordal graphs (containing all interval graphs), 1-split graphs (containing all split graphs) and chordal graphs of diameter at most 2, we are able to decide T 3-S efficiently.     

Iterative RELIEF for feature weighting: algorithms, theories, and applications

RELIEF is considered one of the most successful algorithms for assessing the quality of features. In this paper, we propose a set of new feature weighting algorithms that perform significantly better than RELIEF, without introducing a large increase in computational complexity. Our work starts from a mathematical interpretation of the seemingly heuristic RELIEF algorithm as an online method solving a convex optimization problem with a margin-based objective function. This interpretation explains the success of RELIEF in real application and enables us to identify and address its following weaknesses. RELIEF makes an implicit assumption that the nearest neighbors found in the original feature space are the ones in the weighted space and RELIEF lacks a mechanism to deal with outlier data. We propose an iterative RELIEF (I-RELIEF) algorithm to alleviate the deficiencies of RELIEF by exploring the framework of the expectation-maximization algorithm. We extend I-RELIEF to multiclass settings by using a new multiclass margin definition. To reduce computational costs, an online learning algorithm is also developed. Convergence analysis of the proposed algorithms is presented. The results of large-scale experiments on the UCI and microarray data sets are reported, which demonstrate the effectiveness of the proposed algorithms, and verify the presented theoretical results     

Parallel coloring of graphs: two approximate algorithms

Graph coloring is an abstraction of scheduling problems. Using an exclusive-read and exclusive-write (EREW) parallel random access machine (PRAM) model, two approximate coloring algorithms are parallelized. The performance analysis reveals that the parallel largest-degree-first algorithm is efficient for regular or near-regular graphs; while the second, a costlier but more easily parallelizable algorithm, yields optimal speedup for graphs of widely varying densities.     

Representing uncertain data: models, properties, and algorithms

In general terms, an uncertain relation encodes a set of possible certain relations. There are many ways to represent uncertainty, ranging from alternative values for attributes to rich constraint languages. Among the possible models for uncertain data, there is a tension between simple and intuitive models, which tend to be incomplete, and complete models, which tend to be nonintuitive and more complex than necessary for many applications. We present a space of models for representing uncertain data based on a variety of uncertainty constructs and tuple-existence constraints. We explore a number of properties and results for these models. We study completeness of the models, as well as closure under relational operations, and we give results relating closure and completeness. We then examine whether different models guarantee unique representations of uncertain data, and for those models that do not, we provide complexity results and algorithms for testing equivalence of representations. The next problem we consider is that of minimizing the size of representation of models, showing that minimizing the number of tuples also minimizes the size of constraints. We show that minimization is intractable in general and study the more restricted problem of maintaining minimality incrementally when performing operations. Finally, we present several results on the problem of approximating uncertain data in an insufficiently expressive model.     

Mining class outliers: concepts, algorithms and applications in CRM

Outliers, or commonly referred to as exceptional cases, exist in many real-world databases. Detection of such outliers is important for many applications and has attracted much attention from the data mining research community recently. However, most existing methods are designed for mining outliers from a single dataset without considering the class labels of data objects. In this paper, we consider the class outlier detection problem ‘given a set of observations with class labels, find those that arouse suspicions, taking into account the class labels’. By generalizing two pioneer contributions [Proc WAIM02 (2002); Proc SSTD03] in this field, we develop the notion of class outlier and propose practical solutions by extending existing outlier detection algorithms to this case. Furthermore, its potential applications in CRM (customer relationship management) are also discussed. Finally, the experiments in real datasets show that our method can find interesting outliers and is of practical use.     

Efficient algorithms for (3, 1) graphs

In this paper, we define a class of graphs which are referred to as (3, 1) graphs. A graph is a member of this class if it has the property that within each set of three vertices, there is at least one edge. We derive a lower bound for the size of a maximum clique in a (3, 1) graph as well as an upper bound for the size of a minimum clique covering. In addition, we show that there exists a linear algorithm for constructing a Hamiltonian circuit in a connected (3, 1) graph and an n⁴-algorithm for finding a minimum coloring in a (3, 1) graph.     

An experimental study of scheduling algorithms for many-task applications

The Journal of Supercomputing - The paper studies the performance of algorithms for scheduling of many-task applications in distributed computing systems. Two important classes of such applications...