33924916
Geometric Algorithms for Density-Based Data Clustering
We present new geometric approximation and exact algorithms for the density-based data clustering problem in d-dimensional space Rd (for any constant integer d ? 2). Previously known algorithms for this problem are efficient only for uniformly-distributed points. However, these algorithms all run in ?(n2) time in the worst case, where n is the number of input points. Our approximation algorithm based on the ?-fuzzy distance function takes O(n log n) time for any given fixed value ? > 0, and our exact algorithms take sub-quadratic time. The running times and output quality of our algorithms do not depend on any particular data distribution. We believe that our fast approximation algorithm is of considerable practical importance, while our sub-quadratic exact algorithms are more of theoretical interest. We implemented our approximation algorithm and the experimental results show that our approximation algorithm is efficient on arbitrary input point sets.
31739418
Geometric Algorithms for Density-based Data Clustering
Data clustering is a fundamental problem arising in many practical applications. In this paper, we present new geometric approximation and exact algorithms for the density-based data clustering problem in d-dimensional space ℝd (for any constant integer d ≥ 2). Previously known algorithms for this problem are efficient only when the specified range around each input point, called the δ-neighborhood, contains on average a constant number of input points. Different distributions of the input data points have significant impact on the efficiency of these algorithms. In the worst case when the data points are highly clustered, these algorithms run in quadratic time, although such situations might not occur very frequently on real data. By using computational geometry techniques, we develop faster approximation and exact algorithms for the density-based data clustering problem in ℝd. In particular, our approximation algorithm based on the ∊-fuzzy distance function takes O(n log n) time for any given fixed value ∊>0, and our exact algorithms take sub-quadratic time. The running times and output quality of our algorithms do not depend on any particular data distribution. We believe that our fast approximation algorithm is of considerable practical importance, while our sub-quadratic exact algorithms are more of theoretical interest. We implemented our approximation algorithm and the experimental results show that our approximation algorithm is efficient on arbitrary input point sets.
5196479
Odd Wheels in Graphs
For k?1 the odd wheel of 2k+1 spokes, denoted by W2k+1, is the graph obtained from a cycle of length 2k+1 by adding a new vertex and joining it to all vertices of the cycle. In this paper it is shown that if a graph G of order n with minimum degree greater than 7n/12 is at least 4-chromatic then G contains an odd wheel with at most 5 spokes.
11402970
On structure of graphs embedded on surfaces of nonnegative characteristic with application to choosability
In this paper, we prove a structural theorem of Lebesgue's type concerning some unavoidable configurations for graphs which can be embedded on surfaces of nonnegative characteristic and in which no two 3-cycles share a common vertex. As a corollary, we get a result about choosability of graphs embedded in surface of positive characteristic.
32570723
Parallel algorithm for mining fuzzy association rules
The principle and steps of the algorithm for mining fuzzy association rules is studied, and the parallel algorithm for mining fuzzy association rules is presented. In this parallel mining algorithm, quantitative attributes are partitioned into several fuzzy sets by the parallel fuzzy c-means algorithm, and fuzzy sets are applied to soften the partition boundary of the attributes. Then, the parallel algorithm for mining Boolean association rules is improved to discover frequent fuzzy attributes. Last, the fuzzy association rules with at least fuzzy confidence are generated on all processors. The parallel mining algorithm is implemented on the distributed linked PC/workstation. The experiment results show that the parallel mining algorithm has fine scaleup, sizeup and speedup.
12925025
The 4-Choosability of Plane Graphs without 4-Cycles'
A graphGis calledk-choosable ifkis a number such that if we give lists ofkcolors to each vertex ofGthere is a vertex coloring ofGwhere each vertex receives a color from its own list no matter what the lists are. In this paper, it is shown that each plane graph without 4-cycles is 4-choosable.
39744832
On signed edge domination numbers of graphs
Abstract Given a graph G=(V,E) , if e=uv∈E , then the closed edge-neighbourhood of e is denoted by N[e]={u′v′∈E|u′=u or v′=v} . A function f : E→{+1,−1} is called the signed edge domination function (SEDF) of G if ∑ e′∈N[e] f(e′)⩾1 for every e∈E . The signed edge domination number γ s ′(G) of G is defined as γ s ′(G)= min {∑ e∈E f(e) | f is an SEDF of G} . Let Ψ(m)= min {γ s ′(H)|H is a graph with |E(H)|=m} . In this paper, we determine the exact value of Ψ(m) for each positive integer m . That is: Ψ(m)=2 1 3 24m+25 +6m+5 6 −m, where ⌈x⌉ denotes the ceiling of x . In addition, we also characterize all connected graphs G with γ s ′(G)=|E(G)| .