46287200
A Parallel Algorithm for Finding a Triconnected Component Separator with an Application
41188840
Finding Double Euler Trails of Planar Graphs in Linear Time
This paper answers an open question in the design of complimentary metal-oxide semiconductor VLSI circuits. The question asks whether a polynomial-time algorithm can decide if a given planar graph has a plane embedding ${\cal E}$ such that ${\cal E}$ has an Euler trail P = e1 e2 ... em and its dual graph has an Euler trail $P^*=e^*_1 e^*_2 \ldots e^*_m$, where $e^*_i$ is the dual edge of ei for i=1,2,...,m. This paper answers this question in the affirmative by presenting a linear-time algorithm.
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.
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 $G$. 


32847785
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+? can be achieved by a quadratic-time algorithm for any given constant ??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 by a low-degree polynomial-time algorithm if no vertex is given a weight, while a ratio of 5 can be achieved by a low-degree polynomial-time algorithm otherwise.
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.
28595321
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, 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 [2]. We show that if the maximum radius is no more than a constant times the minimum radius, then there exists a polynomial time approximation scheme. Our techniques are based on the width-bounded geometric separator recently developed in [5,6].
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.
3449616
Fast and memory-efficient regular expression matching for deep packet inspection
Packet content scanning at high speed has become extremely important due to its applications in network security, network monitoring, HTTP load balancing, etc. In content scanning, the packet payload is compared against a set of patterns specified as regular expressions. In this paper, we first show that memory requirements using traditional methods are prohibitively high for many patterns used in packet scanning applications. We then propose regular expression rewrite techniques that can effectively reduce memory usage. Further, we develop a grouping scheme that can strategically compile a set of regular expressions into several engines, resulting in remarkable improvement of regular expression matching speed without much increase in memory usage. We implement a new DFA-based packet scanner using the above techniques. Our experimental results using real-world traffic and patterns show that our implementation achieves a factor of 12 to 42 performance improvement over a commonly used DFA- based scanner. Compared to the state-of-art NFA-based implementation, our DFA-based packet scanner achieves 50 to 700 times speedup.
45057829
Preclassification of handwritten Chinese characters based on basic stroke substructures
A method for preclassification of handwritten Chinese characters is presented. A set of basic stroke substructures is defined using the consistent stroke connection relations. A knowledge guided recognition process is employed to identify the types of the extracted basic stroke substructures found in a handwritten character. Then a 1-D character coding scheme is given to represent the character and the code can be also used for character preclassification.
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).