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The paper focuses on mining clusters that are characterized by a lagged relationship between the data objects. We call such clusters lagged co-clusters. A lagged co-cluster of a matrix is a sub matrix determined by a subset of rows and their corresponding lag over a subset of columns. Extracting such subsets (not necessarily successive) may reveal an underlying governing regulatory mechanism. Such...
For improving the detection efficiency of hidden information blind detection system, an improved hidden information detection method based rough set theory is proposed against the high dimension of statistical features and high relevance about images. First, an improved general steganalysis system framework is proposed with practical method and steps; second, the Algorithm based on the rough set theory...
We prove a new lower bound for the decision complexity of a complex algebraic set in terms of the sum of its (compactly supported) Betti numbers, which is for the first time better than logarithmic. We apply this result to subspace arrangements including some well studied problems such as the knapsack and element distinctness problems.
Given a graph G = (V, E) with real-valued edge weights, the problem of correlation k-clustering with pre-clustered items is to extend a k-clustering of distinguished vertices of G (pre-clustered items) to partition all the vertices into clusters so as to minimize the total absolute weight of cut positive edges and uncut negative edges. This problem for general graphs is APX-complete. A polynomial...
We present new combinatorial algorithms for Boolean matrix multiplication (BMM) and preprocessing a graph to answer independent set queries. We give the first asymptotic improvements on combinatorial algorithms for dense BMM in many years, improving on the "Four Russians'' O(n3/(w log n)) bound for machine models with word size w. (For a pointer machine, we can set w = log n.) The algorithms...
This paper addresses the problems of minimizing nonnegative submodular functions under covering constraints, which generalize the vertex cover, edge cover, and set cover problems. We give approximation algorithms for these problems exploiting the discrete convexity of submodular functions. We first present a rounding 2-approximation algorithm for the submodular vertex cover problem based on the half-integrality...
Let F be a field and f1,..., fk in F[x1, ..., xn] be a set of k polynomials of degree d in n variables over the field F. These polynomials are said to be algebraically dependent if there exists a nonzero k-variate polynomial A(t1, ..., tk) in F[t1, ..., tk] such that A(f1, ..., fk) = 0. A is then called an (f1, ..., fk)-annihilating polynomial. Within computer science, the notion of algebraic dependence...
The elements of discernibility matrix are used as the heuristic information by all the existing attribute reduction algorithms based on discernibility matrix. The time and space complexities of this kind of algorithms are O(\C\2|U\2). To lower the time and space complexities, the simplified decision table and simplified discernibility matrix is introduced, and proved that the non-empty elements of...
Data conversion between different data sets is an important research issue in computer science. Because of its computational complexity and demand for high accuracy, many data conversion problems arising in application can not be solved effectively. Based on the analysis of construction method, a new bijective function hn from natural numbers set N and its n-ary Cartesian product set Nn has been proposed...
In recent years, the fooling set technique has been used to find the lower bounds for nondeterministic state complexity of regular languages. For regular languages in general, the decision version of this problem has not been classified into a certain exact complexity group, but has been proved to be NP-hard and be contained in PSPACE. In this article, fooling set problem of unary regular language...
The deletion-contraction algorithm is perhaps the most popular method for computing a host of fundamental graph invariants such as the chromatic, flow, and reliability polynomials in graph theory, the Jones polynomial of an alternating link in knot theory, and the partition functions of the models of Ising, Potts, and Fortuin-Kasteleyn in statistical physics. Prior to this work, deletion-contraction...
We study two containment problems related to the quantified constraint satisfaction problem (QCSP). Firstly, we give a combinatorial condition on finite structures A and B that is necessary and sufficient to render QCSP(A) a subset of QCSP(B). The required condition is the existence of a positive integer r such that there is a surjective homomorphism from the power structure A^r to B. We note that...
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