The previously introduced multiset language classes defined by multiset storage automata are being explored with respect to their closure properties and alternative characterizations.

Set variables in constraint satisfaction problems (CSPs) are typically propagated by enforcing set bounds consistency together with cardinality reasoning, which uses some inference rules involving the cardinality of a set variable to produce more prunings than set bounds propagation alone. Multiset variables are a generalization of set variables by allowing the elements to have repetitions. In ...

Graphs are discrete structures that model relationships between objects. Graphs play an important role in many areas of computer science. In this reading we introduce basic notions of graph theory that are important in computer science. In particular we look directed graphs, undirected graphs, trees and some applications of graphs. We begin by discussing directed graphs, also known as digraphs....

We solve the problem of designing an O(1) time algorithm for generating adjacent multiset combinations in a different approach from Walsh [17]. By the word “adjacent”, we mean that two adjacent multiset combinations are different at two places by one in their vector forms. Previous O(1) time algorithms for multiset combinations generated non-adjacent multiset combinations. Our algorithm in this...

For positive integers and , consider a multiset of nonempty subsets such that there is unique partition these into partitions . We study the maximum possible size multiset. focus on regime show When for any this lower bound simplifies to we matching upper optimal up factor also compute exactly when

This paper describes two- and multiset canonical correlations analysis (CCA) for data fusion, multisource, multiset, or multitemporal exploratory data analysis. These techniques transform multivariate multiset data into new orthogonal variables called canonical variates (CVs) which, when applied in remote sensing, exhibit ever-decreasing similarity (as expressed by correlation measures) over se...