<abstract xmlns="http://www.w3.org/1999/xhtml">In this study, a mathematical model is presented for an online data clustering problem. Data clustering plays an important role in many applications like handling the data acknowledgment problem and data stream management in real-time locating systems. The inputs in these problems are data sequences, each containing several data elements. Each data element has an arrival time and a weight that reflects its importance. The arrival times are not known in advance, and some data elements never arrive. Hence the system should decide which moment is optimal for forwarding the collected data for processing. This requires finding a good trade-off between the amount of collected information and the waiting time, which may be regarded as a minimization problem. Here, we investigate several online algorithms and present their competitive analysis and average case studies. Experimental results, based on simulations using artificially generated data, are also presented and they confirm the efficiency of our methods.</abstract>

A new model for the linear 1-dimensional online clustering problem

<abstract xmlns="http://www.w3.org/1999/xhtml">Let G be a non-trivial, simple, finite, connected and undirected graph of order n and size m. An induced acyclic graphoidal decomposition (IAGD) of G is a collection ψ of non-trivial and internally disjoint induced paths in G such that each edge of G lies in exactly one path of ψ. For a labeling f : V → {1, 2, 3, . . . ,n}, let ↑ Gf be the directed graph obtained by orienting the edges uv of G from u to v, provided f(u) &lt; f(v). If the set ψf of all maximal directed induced paths in ↑ Gf with directions ignored is an induced path decomposition of G, then f is called an induced graphoidal labeling of G and G is called an induced label graphoidal graph. The number ηil = min{|ψf| : f is an induced graphoidal labeling of G} is called the induced label graphoidal decomposition number of G. In this paper we introduce and study the concept of induced graphoidal labeling as an extension of graphoidal labeling.</abstract>

Department of Mathematics, The Madura College, Madurai-11

Department of Mathematics, Christ University, Bangalore-29 India

Induced label graphoidal graphs

<abstract xmlns="http://www.w3.org/1999/xhtml">The A** algorithm is a famous heuristic path-finding algorithm. In this paper its different definitions will be analyzed firstly. Then its memory complexity is going to be investigated. On the one hand, the well-known concept of better-information will be extended to compare the different heuristics in the A** algorithm. On the other hand, a new proof will be given to show that there is no deterministic graph-search algorithm having better memory complexity than A**∗. At last the time complexity of A** will be discussed.</abstract>

Remarks on the A** algorithm

<abstract xmlns="http://www.w3.org/1999/xhtml">We show that the problem of deciding whether the edge set of a bipartite graph can be partitioned into three matchings, of size k1, k2 and k3 is NP-complete, even if one of the matchings is required to be perfect. We also show that the problem of deciding whether the edge set of a simple graph contains a perfect matching and a disjoint matching of size k or not is NP-complete, already for bipartite graphs with maximum degree 3. It also follows from our construction that it is NP-complete to decide whether in a bipartite graph there is a perfect matching and a disjoint matching that covers all vertices whose degree is at least 2.</abstract>

Partitioning to three matchings of given size is NP-complete for bipartite graphs

<abstract xmlns="http://www.w3.org/1999/xhtml">The score set of a tournament is defined as the set of its different outdegrees. In 1978 Reid [15] published the conjecture that for any set of nonnegative integers D there exists a tournament T whose degree set is D. Reid proved the conjecture for tournaments containing n = 1, 2, and 3 vertices. In 1986 Hager [4] published a constructive proof of the conjecture for n = 4 and 5 vertices. In 1989 Yao [18] presented an arithmetical proof of the conjecture, but general polynomial construction algorithm is not known. In [6] we described polynomial time algorithms which reconstruct the score sets containing only elements less than 7. In [5] we improved this bound to 9. In this paper we present and analyze new algorithms Hole-Map, Hole-Pairs, Hole-Max, Hole-Shift, Fill-All, Prefix-Deletion, and using them improve the above bound to 12, giving a constructive partial proof of Reid’s conjecture.</abstract>

Reconstruction of score sets

<abstract xmlns="http://www.w3.org/1999/xhtml">We apply the concept of statistical complexity to understand the dynamical behaviour of the time series by the probability distribution. This quantity allows to distinguish between the random, regular motion and the structural complexity in finite systems. We determined the numerical approximation of the statistical complexity of the Lozi attractor and the generalized number system</abstract>

Statistical complexity and generalized number system

<abstract xmlns="http://www.w3.org/1999/xhtml">Using different definitions of split graphs we propose quick algorithms for the recognition and extremal reconstruction of split sequences among integer, regular, and graphic sequences.</abstract>

University of Kashmir Hazratbal Srinagar-190006, India

Eötvös Loránd University Faculty of Informatics, H-1011 Budapest, Pázmány s. 1/A, Hungary

Recognition of split-graphic sequences

<abstract xmlns="http://www.w3.org/1999/xhtml">Finding frequent sequential patterns has been defined as finding ordered list of items that occur more times in a database than a user defined threshold. For big and dense databases that contain really long sequences and large itemset such as medical case histories, algorithm proposed on this idea of counting the occurrences output enourmous number of highly redundant frequent sequences, and are therefore simply impractical. Therefore, there is a need for algorithm that perform frequent pattern search and prefiltering simultaneously. In this paper, we propose an algorithm that reinterprets the term support on text mining basis. Experiments show that our method not only eliminates redundancy among the output sequences, but it scales much better with huge input data sizes. We apply our algorithm for mining medical databases: what diagnoses are likely to lead to a certain future health condition.</abstract>

Finding sequential patterns with TF-IDF metrics in health-care databases

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