14422953
On-line learning of rectangles
This paper solves the following open problem: Is there an algorithmfor on-line learning of rectangles <inline-equation><f><pr align="c"><ll>i=1</ll><ul>d</ul></pr></f><?Pub Caret></inline-equation><?Pub Fmt italic>a<subscrpt>i</subscrpt>,a<subscrpt>i</subscrpt>+1,…,b<subscrpt>i</subscrpt>}<?Pub Fmt /italic>over a discrete domain<?Pub Fmt italic>{1,…,n}<supscrpt>d</supscrpt><?Pub Fmt /italic>whose error bound is polylogarithmic in the size<?Pub Fmt italic>n<supscrpt>d</supscrpt><?Pub Fmt /italic> of the domain(i.e. polynomial in <?Pub Fmt italic>d<?Pub Fmt /italic> and log<?Pub Fmt italic>n<?Pub Fmt /italic> )? We give a positive solution byintroducing a new design technique that appears to be of some intereston its own. The new learning algorithm for rectangles consists of<?Pub Fmt italic>2d<?Pub Fmt /italic> separate search strategies thatsearch for the parameters <?Pub Fmt italic>a<subscrpt>1</subscrpt>,b<subscrpt>1</subscrpt>,…,a<subscrpt>d</subscrpt>,b<subscrpt>d</subscrpt><?Pub Fmt /italic>of the target rectangle. A learning algorithm with this type of modulardesign ends to fail because of the well known “credit assignmentproblem”: Which of the <?Pub Fmt italic>2d<?Pub Fmt /italic> localsearch strategies should be “blamed” when the globalalgorithm makes an error? We overcome this difficulty by employing localsearch strategies (“error tolerant binary search”) that areable to tolerate certain types of wrong credit assignments.
Section 4 contains another application of this design technique: analgorithm for learning the union of two rectangles in the plane.
29625123
A PTAS for a disc covering problem using width-bounded separators
In this paper, we study the following disc covering problem: Given a set of discs of various radii on the plane and centers on the grid points, find a subset of discs to maximize the area covered by exactly one disc. This problem originates from the application in digital halftoning, with the best known approximation factor being 5.83 (Asano et al., 2004). We show that if their radii are between two positive constants, then there exists a polynomial time approximation scheme. Our techniques are based on the width-bounded geometric separator recently developed in Fu and Wang (2004), Fu (2006).
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.
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
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.
7765043
WebSail: From On-line Learning to Web Search
In this paper we report our research on building WebSail, an intelligent web search engine that is able to perform real-time adaptive learning. WebSail learns from the user's relevance feedback, so that it is able to speed up its search process and to enhance its search performance. We design an efficient adaptive learning algorithm TW2 to search for web documents. WebSail employs TW2 together with an internal index database and a real-time meta-searcher to perform real-time adaptive learning to find desired documents with as little relevance feedback from the user as possible. The architecture and performance of WebSail are also discussed.
20004613
Disk Embeddings of Planar Graphs
Abstract 
Given a planar graph $G=(V,E)$ and a rooted forest ${\FF}=(V_{\FF}, A_{\FF})$ 
with leaf set $V$, we wish to decide whether $G$ has a plane embedding $\GG$ 
satisfying the following condition: There are $|V_{\FF}|-|V|$ pairwise noncrossing 
Jordan curves in the plane one-to-one corresponding to the nonleaf vertices of 
${\FF}$ such that for every nonleaf vertex $f$ of ${\FF}$, the interior of the curve 
$\JJ_f$ corresponding to $f$ contains all the leaf descendants of $f$ in ${\FF}$
but contains no other leaves of ${\FF}$. 
This problem arises from theoretical studies in geographic database systems. 
It is unknown whether this problem can be solved in polynomial time. 
This paper presents an almost linear-time algorithm for a nontrivial special case 
where the set of leaf descendants of each nonleaf vertex $f$ in ${\FF}$ induces 
a connected subgraph of $G$. 


28886116
A Linear-Time Algorithm for 7-Coloring 1-Plane Graphs
AbstractA graph G is 1-planar if it can be embedded in the plane in such a way 
that each edge crosses at most one other edge. Borodin showed that 
1-planar graphs are 6-colorable, but his proof does not lead to a linear-time 
algorithm. This paper presents a linear-time algorithm for 7-coloring 
1-plane graphs (which are 1-planar graphs already embedded in the plane). 
The main difficulty in the design of our algorithm comes from 
the fact that the class of 1-planar graphs is not closed under the 
operation of edge contraction. This difficulty is overcome by a structural 
lemma that may be useful in other problems on 1-planar graphs. This paper 
also shows that it is NP-complete to decide whether a given 1-planar graph 
is 4-colorable. The complexity of the problem of deciding whether a given 
1-planar graph is 5-colorable is still unknown.
5754331
Web-page summarization using clickthrough data
Most previous Web-page summarization methods treat a Web page as plain text. However, such methods fail to uncover the full knowledge associated with a Web page needed in building a high-quality summary, because many of these methods do not consider the hidden relationships in the Web. Uncovering the hidden knowledge is important in building good Web-page summarizers. In this paper, we extract the extra knowledge from the clickthrough data of a Web search engine to improve Web-page summarization. Wefirst analyze the feasibility in utilizing the clickthrough data to enhance Web-page summarization and then propose two adapted summarization methods that take advantage of the relationships discovered from the clickthrough data. For those pages that are not covered by the clickthrough data, we design a thematic lexicon approach to generate implicit knowledge for them. Our methods are evaluated on a dataset consisting of manually annotated pages as well as a large dataset that is crawled from the Open Directory Project website. The experimental results indicate that significant improvements can be achieved through our proposed summarizer as compared to the summarizers that do not use the clickthrough data.
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.
5899080
Optimizing Web Search Using Spreading Activation on the Clickthrough Data
In this paper, we propose a mining algorithm to utilize the user click-through data to improve search performance. The algorithm first explores the relationship between queries and Web pages and mine out co-visiting relationship as the virtual link among the Web pages, and then Spreading Activation mechanism is used to perform the query-dependent search. Our approach could overcome the challenges discussed above and the experimental results on a large set of MSN click-through log data show a significant improvement on search performance over the DirectHit algorithm as well as the baseline search engine.