In a total order of the vertices of a graph, two edges with no endpoint in common can be crossing, nested, or disjoint. A k-stack (respectively, k-queue, k-arch) layout of a graph consists of a total order of the vertices, and a partition of the edges into k sets of pairwise non-crossing (respectively, non-nested, non-disjoint) edges. Motivated by numerous applications, stack layouts (also call...

All the recent available graph partitioning packages include the multilevel graph partition algorithm in which the graph is coarsened by a sequence of increasingly smaller graphs. The smallest graph is partitioned using a graph partitioning algorithm and this partition is propagated back through the hierarchy of graphs. A Kernighan –Lin algorithm is applied periodically to refine the partition....

Many hierarchical techniques to solve large Markov decision processes (MDPs) are based on the partition of the state space into strongly connected components (SCCs) that can be classified into some levels. In each level, smaller problems named restricted MDPs are solved, and then these partial solutions are combined to obtain the global solution. In this paper, we first propose a novel algorith...

– Partitioning clustering algorithms, construct non-overlapping clusters such that each item is assigned to exactly one cluster. Example: k-means – Agglomerative clustering algorithms construct a hierarchical set of nested clusters, indicating the relatedness between clusters. Example: hierarchical clustering • In classification, we partition data into known labels. For example, we might constr...

We consider the problem of partitioning the vertex-set of a tree to p parts to minimize a cost function. Since the number of partitions is exponential in the number of vertices, it is helpful to identify small classes of partitions which also contain optimal partitions. Two such classes, called consecutive partitions and nested partitions, have been well studied for the set partition problem, w...

Nowadays task partition for parallel computing is becoming more and more important. Particular in power system dynamic simulation, it is critical to design an efficient partition algorithm to reduce the communication and balance the computation load [1]. This paper presents a novel multilevel partition scheme based on the graph partition algorithm. By introducing regional characteristic into th...

In this paper, we first define the correlated table of an SQL query without nested subqueries which extends the result set of an SQL query to a set of result sets, one for each distinct binding tuple. We then present an algorithm to convert any SQL query with nested subqueries to a correlated query without nested subqueries. The proposed algorithm provides a simple but very effective method unn...

A method is proposed for classification to ordinal categories by applying the search partition analysis (SPAN) approach. It is suggested that SPAN be repeatedly applied to binary outcomes formed by collapsing adjacent categories of the ordinal scale. By a simple device, whereby successive binary partitions are constrained to be nested, a partition for classification to the ordinal states is obt...

We propose a nonparametric Bayesian local clustering (NoB-LoC) approach for heterogeneous data. NoB-LoC implements inference for nested clusters as posterior inference under a Bayesian model. Using protein expression data as an example, the NoB-LoC model defines a protein (column) cluster as a set of proteins that give rise to the same partition of the samples (rows). In other words, the sample...

A novel strategy for hierarchical speech recognition is proposed in this paper. Based on space partition, it takes the advantage of each recognizer on subspace. It organizes recognizers in a manner of nested recursion. Experiment results show that the final performance of the new method can reach an error reduction about 33% compared with the best recognizer.