32200257
Partial difference sets
A (?,k,?,β)-partial difference set in a finite group G of order ? is a subset D of G with k distinct elements such that expressions dnd?12 for d1 and d2 in D, represent each non-identity element not contained in D exactly ? times and each non-identity element contained in D exactly ?+β times. Such a set is closely related to association schemes of PBIB designs with two associate classes.
44609559
Cyclic Relative Difference Sets with Classical Parameters
We investigate the existence of cyclic relative difference sets with parameters ((qd?1)/(q?1), n, qd?1, qd?2(q?1)/n), q any prime power. One can think of these as “liftings” or “extensions” of the complements of Singer difference sets. When q is odd or d is even, we find that relative difference sets with these parameters exist if and only if n is a divisor of q?1. In case q is even and d is odd, relative difference sets with these parameters exist if and only if n is a divisor of 2(q?1).
17213172
A New Fast Clustering Algorithm Based on Reference and Density
Density-based clustering is a sort of clustering analysis methods, which can discover clusters with arbitrary shape and is insensitive to noise data. The efficiency of data mining algorithms is strongly needed with data becoming larger and larger. In this paper, we present a new fast clustering algorithm called CURD, which means Clustering Using References and Density. Its creativity is capturing the shape and extent of a cluster with references, and then it analyzes the data based on the references. CURD preserves the ability of density based clustering method’s good advantages, and it is much efficient because of its nearly linear time complexity, so it can be used in mining very large databases. Both our theoretic analysis and experimental results confirm that CURD can discover clusters with arbitrary shape and is insensitive to noise data; In the meanwhile, its executing efficiency is much higher than R*-tree based DBSCAN algorithm.