6825045
Learning Counting Functions with Queries
Abstract We investigate the problem of learning disjunctions of counting functions, which are general cases of parity and modulo functions, with equivalence and membership queries. We prove that, for any prime number p , the class of disjunctions of integer-weighted counting functions with modulus p over the domain Z q n (or Z n ) for any given integer q ⩾ 2 is polynomial time learnable using at most n + 1 equivalence queries, where the hypotheses issued by the learner are disjunctions of at most n counting functions with weights from Z p . In general, a counting function may have a composite modulus. We prove that, for any given integer q ⩾ 2, over the domain Z 2 n , the class of read-once disjunctions of Boolean-weighted counting functions with modulus q is polynomial-time learnable with only one equivalence query and O( n q ) membership queries.
7399730
An Almost Linear Time 2.8334-Approximation Algorithm for the Disc Covering Problem
The disc covering problem asks to cover a set of points on the plane with a minimum number of fix-sized discs. We develop an O(n(logn)2(loglogn)2) deterministic time 2.8334-approximation algorithm for this problem. Previous approximation algorithms [7,3,6], when used to achieve the same approximation ratio for the disc covering problem, will have much higher time complexity than our algorithms.
44651708
Personalized Web Search with Clusters
28060413
The Architecture of Yarrow: A Real-Time Intelligent Meta-Search Engine
140623
Optimal Algorithms for Finding User Access Sessions from Very Large Web Logs
Although efficient identification of user access sessions from very large web logs is an unavoidable data preparation task for the success of higher level web log mining, little attention has been paid to algorithmic study of this problem. In this paper we consider two types of user access sessions, interval sessions and gap sessions. We design two efficient algorithms for finding respectively those two types of sessions with the help of some proposed structures. We present theoretical analysis of the algorithms and prove that both algorithms have optimal time complexity and certain error-tolerant properties as well. We conduct empirical performance analysis of the algorithms with web logs ranging from 100 megabytes to 500 megabytes. The empirical analysis shows that the algorithms just take several seconds more than the baseline time, i.e., the time needed for reading the web log once sequentially from disk to RAM, testing whether each user access record is valid or not, and writing each valid user access record back to disk. The empirical analysis also shows that our algorithms are substantially faster than the sorting based session finding algorithms. Finally, optimal algorithms for finding user access sessions from distributed web logs are also presented.
5722664
A Visualization System using Data Mining Techniques for Identifying Information Sources
The Visual Analysis System (VAS) was developed to couple emerging successes in data mining with information visualization techniques in order to create a richly interactive environment for information retrieval from the World Wide Web. VAS's retrieval strategy operates by first using a conventional search engine to form a core set,of retrieved documents. This core set is expanded by crawling from links in these documents to form a much larger set. The link topology of the larger set is then examined using data mining techniques to identify pages likely to be both relevant to the query and reliable as sources of information. Information visualization techniques are used to display the filtered set in a form amenable to the use of perceptual processes to filter and guide further user directed search. (Contains 16 references.) (MES) Reproductions supplied by EDRS are the best that can be made from the original document. N tr) 00 7171A Visualization System using Data Mining Techniques for Identifying Information Sources Richard H. Fowler, Tarkan Karadayi, Zhixiang Chen, Xiannong Meng, Wendy A. Lawrence Fowler Department of Computer Science University of Texas Pan American United States {fowler, tkaradayi, chen, meng, wfowler @panam.edu} PERMISSION TO REPRODUCE AND DISSEMINATE THIS MATERIAL HAS BEEN GRANTED BY
15432149
Ubiquitous media agents for managing personal multimedia files
A novel idea of ubiquitous media agents is presented. Media agents are intelligent systems that are able to automatically collect and build personalized semantic indices of multimedia data on behalf of the user whenever and wherever he/she accesses/uses these multimedia data. The sources of these semantic descriptions are the textual context of the same documents that contain these multimedia data. The URLs of these multimedia data are indexed using these textual features. When the user wants to use these multimedia data once again, the media agents can also help the user find relevant multimedia data and provide proper suggestions based on the semantic indices. The media agents can also learn form the user's interaction records to refine the semantic indices and to model the user intentions and preferences. In our experiments, the media agents are effective in gathering relevant semantics for media objects and learning to provide precise suggestions when the user wants to re-use relevant media objects again.
5311208
Domain decomposition algorithms for mixed methods for second-order elliptic problems
Domain decomposition algorithms for mixed finite element methods for linear second-order elliptic problems in R 2 and R 3 are developed. A convergence theory for two-level and multilevel Schwarz methods applied to the algorithms under consideration is given. It is shown that the condition number of these iterative methods is bounded uniformly from above in the same manner as in the theory of domain decomposition methods for conforming and nonconforming finite element methods for the same differential problems. Numerical experiments are presented to illustrate the present techniques.
701
Common-Face Embeddings of Planar Graphs
Given a planar graph $\Ggg$ and a sequence ${\CC}_1,\ldots,{\CC}_q$, where each ${\CC}_i$ is a family of vertex subsets of $\Ggg$, we wish to find a plane embedding of $\Ggg$, if any exists, such that, for each $i\in\{1,\ldots,q\}$, there is a face Fi in the embedding whose boundary contains at least one vertex from each set in CCi. This problem has applications in the recovery of topological information from geographical data and the design of constrained layouts in VLSI. Let $\inputsize$ be the input size, i.e., the total number of vertices and edges in $\Ggg$ and the families CCi, counting multiplicity. We show that this problem is NP-complete in general. We also show that it is solvable in $O(\inputsize\log \inputsize)$ time for the special case in which, for each input family CCi, each set in CCi induces a connected subgraph of the input graph $\Ggg$. Note that the classical problem of simply finding a planar embedding is a further special case of this case with q=0. Therefore, the processing of the additional constraints CC1, . . .,CCq incurs only a logarithmic factor of overhead.
38006851
Approximation Algorithms for Independent Sets in Map Graphs
This paper presents polynomial-time approximation algorithms for the problem of computing a maximum independent set in a given map graph G with or without weights on its vertices. If G is given together with a map, then a ratio of 1+δ can be achieved in O(n2) time for any given constant δ > 0, no matter whether each vertex of G is given a weight or not. In case G is given without a map, a ratio of 4 can be achieved in O(n7) time if no vertex is given a weight, while a ratio of O(log n) can be achieved in O(n7 log n) time otherwise. Behind the design of our algorithms are several fundamental results for map graphs; these results can be used to design good approximation algorithms for coloring and vertex cover in map graphs, and may find applications to other problems on map graphs as well.
207130305
On k-pairable graphs
Motivated by a 1994 result of Graham et al. (Amer. Math. Monthly 101(7) (1994) 664) about spanning trees of the graphs with an antipodal isomorphism, we introduce the concept of k-pairable graphs and extend the result in Graham et al. (Amer. Math. Monthly 101(7) (1994) 664) to this larger class of graphs. We then define a new graph parameter p(G), called the pair length of graph G. This parameter measures the maximum distance, in some sense, between a subgraph induced by half the vertices of G with the isomorphic subgraph induced by the other half of V(G). An upper bound for the parameter p(G) is given. Some properties of the k-pairable graphs and their product graphs are studied. We also post some problems for further research.