52799334
On the Editing Distance Between Undirected Acyclic Graphs
We consider the problem of comparing CUAL graphs (Connected, Undirected, Acyclic graphs with nodes being Labeled). This problem is motivated by the study of information retrieval for bio-chemical and molecular databases. Suppose we define the distance between two CUAL graphs G1 and G2 to be the weighted number of edit operations (insert node, delete node and relabel node) to transform G1 to G2. By reduction from exact cover by 3-sets, one can show that finding the distance between two CUAL graphs is NP-complete. In view of the hardness of the problem, we propose a constrained distance metric, called the degree-2 distance, by requiring that any node to be inserted (deleted) have no more than 2 neighbors. With this metric, we present an efficient algorithm to solve the problem. The algorithm runs in time O(N1N2D2) for general weighting edit operations and in time for integral weighting edit operations, where Ni, i=1, 2, is the number of nodes in Gi, D=min{d1, d2} and di is the maximum degree of Gi.
11616193
Automatic Hierarchical Classification of Structured Deep Web Databases
We present a method that automatically classifies structured deep Web databases according to a pre-defined topic hierarchy. We assume that there are some manually classified databases, i.e., training databases, in every node of the topic hierarchy. Each training database is probed using queries constructed from the node titles of the topic hierarchy and the query result counts reported by the database are used to represent the content of the database. Hence, when adding a new database it can be probed by the same set of queries and classified to a node whose training databases are most similar to the new one. Specifically, a support vector machine classifier is trained on each internal node of the topic hierarchy with these training databases and the new database can be classified into the hierarchy top-down level by level. A feature extension method is proposed to create discriminant features. Experiments run on real structured Web databases collected from the Internet show that this classification method is quite accurate.
12680145
Finding Patterns in Three-Dimensional Graphs: Algorithms and Applications to Scientific Data Mining
Presents a method for finding patterns in 3D graphs. Each node in a graph is an undecomposable or atomic unit and has a label. Edges are links between the atomic units. Patterns are rigid substructures that may occur in a graph after allowing for an arbitrary number of whole-structure rotations and translations as well as a small number (specified by the user) of edit operations in the patterns or in the graph. (When a pattern appears in a graph only after the graph has been modified, we call that appearance "approximate occurrence.") The edit operations include relabeling a node, deleting a node and inserting a node. The proposed method is based on the geometric hashing technique, which hashes node-triplets of the graphs into a 3D table and compresses the label-triplets in the table. To demonstrate the utility of our algorithms, we discuss two applications of them in scientific data mining. First, we apply the method to locating frequently occurring motifs in two families of proteins pertaining to RNA-directed DNA polymerase and thymidylate synthase and use the motifs to classify the proteins. Then, we apply the method to clustering chemical compounds pertaining to aromatic compounds, bicyclicalkanes and photosynthesis. Experimental results indicate the good performance of our algorithms and high recall and precision rates for both classification and clustering.
236203
New Techniques for DNA Sequence Classification
DNA sequence classification is the activity of determining whether or not an unlabeled sequence S belongs to an existing class C. This paper proposes two new techniques for DNA sequence classification. The first technique works by comparing the unlabeled sequence S with a group of active motifs discovered from the elements of C and by distinction with elements outside of C. The second technique generates and matches gapped fingerprints of S with elements of C. Experimental results obtained by running these algorithms on long and well conserved Alu sequences demonstrate the good performance of the presented methods compared with FASTA. When applied to less conserved and relatively short functional sites such as splice-junctions, a variation of the second technique combining fingerprinting with consensus sequence analysis gives better results than the current classifiers employing text compression and machine learning algorithms.
14900181
Unordered tree mining with applications to phylogeny
Frequent structure mining (FSM) aims to discover and extract patterns frequently occurring in structural data, such as trees and graphs. FSM finds many applications in bioinformatics, XML processing, Web log analysis, and so on. We present a new FSM technique for finding patterns in rooted unordered labeled trees. The patterns of interest are cousin pairs in these trees. A cousin pair is a pair of nodes sharing the same parent, the same grandparent, or the same great-grandparent, etc. Given a tree T, our algorithm finds all interesting cousin pairs of T in O(|T|/sup 2/) time where |T| is the number of nodes in T. Experimental results on synthetic data and phylogenies show the scalability and effectiveness of the proposed technique. To demonstrate the usefulness of our approach, we discuss its applications to locating co-occurring patterns in multiple evolutionary trees, evaluating the consensus of equally parsimonious trees, and finding kernel trees of groups of phylogenies. We also describe extensions of our algorithms for undirected acyclic graphs (or free trees).
2286283
Query result ranking over e-commerce web databases
To deal with the problem of too many results returned from an E-commerce Web database in response to a user query, this paper proposes a novel approach to rank the query results. Based on the user query, we speculate how much the user cares about each attribute and assign a corresponding weight to it. Then, for each tuple in the query result, each attribute value is assigned a score according to its "desirableness" to the user. These attribute value scores are combined according to the attribute weights to get a final ranking score for each tuple. Tuples with the top ranking scores are presented to the user first. Our ranking method is domain independent and requires no user feedback. Experimental results demonstrate that this ranking method can effectively capture a user's preferences.
7902129
Efficient Minimization of Numerical Summation Errors
Given a multiset X={x 1,... x n } of real numbers, the floating-point set summation (FPS) problem asks for S n = x 1+...+ x n , and the floating point prefix set summation problem (FPPS) asks for S k =x 1+...+x k for all k = 1, ... n. Let E k * denote the minimum worst-case error over all possible orderings of evaluating S k . We prove that if X has both positive and negative numbers, it is NP-hard to compute S n with the worst-case error equal to E n * . We then give the first known polynomial-time approximation algorithm for computing Sn that has a provably small error for arbitrary X. Our algorithm incurs a worstcase error at most 2([log(n−1)]+1) E n * . After X is sorted, it runs in O(n) time, yielding an O(n 2)-time approximation algorithm for computing S k for all k = 1, ..., n such that the worst-case error for each S k is less than 2(⌈ log(k−1)⌋+ 1)E k * .
205093793
On p-Creative Sets and p-Completely Creative Sets
Abstract We study p-creative sets and p-completely creative sets. We first prove that for recursively enumerable sets, p-creativeness is equivalent to p-complete creativeness and Myhill's theorem still holds in the polynomial setting. We then consider p-creativity and p-complete creativity for time complexity classes. We prove that for P, p-creativeness is equivalent to p-complete creativeness. Moreover, we prove that a set A is p-m-complete for DEXT iff A is p-creative for P in DEXT. Since every p-m-complete set for DEXT is p-1-complete (Berman, 1977), we know that Myhill's theorem still holds for P in DEXT. These results can also be proved for NP in NEXT. k -creative sets and k -completely creative sets in NP are next studied. ( k,l )-creative sets and ( k,l )-completely creative sets in a more general setting are defined and shown to exist. It is known that k -completely creative sets are NP-complete (Joseph and Young, 1985), but it is not known whether the converse is true. We approach this problem based on our “double diagonalization” technique of showing that every p-m-complete set for DEXT is p-creative for P. A new class of k -completely creative sets is constructed as well.
31564513
Packing of Unequal Spheres and Automated Radiosurgical Treatment Planning
We study an optimization problem of packing unequal spheres into a three-dimensional (3D) bounded region in connection with radiosurgical treatment planning. Given an input (R, V, S, L), where R is a 3D bounded region, V a positive integer, S a multiset of spheres, and L a location constraint on spheres, we want to find a packing of R using the minimum number of spheres in S such that the covered volume is at least V; the location constraint L is satisfied; and the number of points on the boundary of R that are touched by spheres is maximized. Such a packing arrangement corresponds to an optimal radiosurgical treatment planning. Finding an optimal solution to the problem, however, is computationally intractable. In particular, we show that this optimization problem and several related problems are NP-hard. Hence, some form of approximations is needed. One approach is to consider a simplified problem under the assumption that spheres of arbitrary (integral) diameters are available with unlimited supply, and there are no location constraints. This approach has met with certain success in medical applications using a dynamic programming algorithm (Bourland and Wu, 1996; Wu, 1996). We propose in this paper an improvement to the algorithm that can greatly reduce its computation cost.
61565821
Modelling and stability of FAST TCP
We introduce a discrete-time model of FAST TCP that fully captures the effect of self-clocking and compare it with the traditional continuous-time model. While the continuous-time model predicts instability for homogeneous sources sharing a single link when feedback delay is large, experiments suggest otherwise. Using the discrete-time model, we prove that FAST TCP is locally asymptotically stable in general networks when all sources have a common round-trip feedback delay, no matter how large the delay is. We also prove global stability for a single bottleneck link in the absence of feedback delay. The techniques developed here are new and applicable to other protocols.
17604851
Efficient point coverage in wireless sensor networks
We study minimum-cost sensor placement on a bounded 3D sensing field, R, which comprises a number of discrete points that may or may not be grid points. Suppose we have ℓ types of sensors available with different sensing ranges and different costs. We want to find, given an integer σ ≥ 1, a selection of sensors and a subset of points to place these sensors such that every point in R is covered by at least σ sensors and the total cost of the sensors is minimum. This problem is known to be NP-hard. Let ki denote the maximum number of points that can be covered by a sensor of the ith type. We present in this paper a polynomial-time approximation algorithm for this problem with a proven approximation ratio $${\gamma = \sum_{i=1}^{\ell} k_{i} -\sigma+1}$$. In applications where the distance of any two points has a fixed positive lower bound, each ki is a constant, and so we have a polynomial-time approximation algorithms with a constant guarantee. While γ may be large, we note that it is only a worst-case upper bound. In practice the actual approximation ratio is small, even on randomly generated points that do not have a fixed positive minimum distance between them. We provide a number of numerical results for comparing approximation solutions and optimal solutions, and show that the actual approximation ratios in these examples are all less than 3, even though γ is substantially larger.