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.
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.
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.
4216648
Optimizing web search using web click-through data
The performance of web search engines may often deteriorate due to the diversity and noisy information contained within web pages. User click-through data can be used to introduce more accurate description (metadata) for web pages, and to improve the search performance. However, noise and incompleteness, sparseness, and the volatility of web pages and queries are three major challenges for research work on user click-through log mining. In this paper, we propose a novel iterative reinforced algorithm to utilize the user click-through data to improve search performance. The algorithm fully explores the interrelations between queries and web pages, and effectively finds "virtual queries" for web pages and overcomes the challenges discussed above. Experiment results on a large set of MSN click-through log data show a significant improvement on search performance over the naive query log mining algorithm as well as the baseline search engine.
17657159
A Chinese-character thinning algorithm based on global features and contour information
This paper proposes a method of using run-length coding to perform thinning. First, we construct graphs from characters. The attributes (vertical lines, horizontal lines or points) of each node in the graph are determined according to the node's relationship to the nodes above and below it (we will refer to these relationships as global features) and the black runs within the node. Intersections between two adjacent segments are determined on the basis of the graph constructed and contour information. The thinning algorithm thus employs global features and contour information to produce a more accurate skeleton.
27655532
On the Planar Two-Watchtower Problem
In this paper we study the following planar two-watchtower problem: given a terrain (X-monotone chain) T with n vertices, locate two vertical segments (watchtowers) uv and u′v′ which have to be erected on T such that every point on T is visible to the top of either watchtowers (u or u′) and the maximum height of uv, u′v′ is minimized. We present an O(n4) time algorithm to solve the discrete version of this problem when v, v′ must be on some vertices of T. Under a mild condition on solving a special cubic equation with three bounded variables in O(f3) time we can also generalize the algorithm to solve the general problem in O(n4 +n3f3) time. Using parametric search, the discrete problem can be solvedin O(n3 log2 n) time and the general problem can be solvedin O(n4 log2 n) time.
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.
16272457
SimFusion: measuring similarity using unified relationship matrix
In this paper we use a Unified Relationship Matrix (URM) to represent a set of heterogeneous data objects (e.g., web pages, queries) and their interrelationships (e.g., hyperlinks, user click-through sequences). We claim that iterative computations over the URM can help overcome the data sparseness problem and detect latent relationships among heterogeneous data objects, thus, can improve the quality of information applications that require com- bination of information from heterogeneous sources. To support our claim, we present a unified similarity-calculating algorithm, SimFusion. By iteratively computing over the URM, SimFusion can effectively integrate relationships from heterogeneous sources when measuring the similarity of two data objects. Experiments based on a web search engine query log and a web page collection demonstrate that SimFusion can improve similarity measurement of web objects over both traditional content based algorithms and the cutting edge SimRank algorithm.