Concepts inA graph-theoretic approach to extract storylines from search results
Graph theory
In mathematics and computer science, graph theory is the study of graphs, mathematical structures used to model pairwise relations between objects from a certain collection. A "graph" in this context is a collection of "vertices" or "nodes" and a collection of edges that connect pairs of vertices.
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Representation (mathematics)
In mathematics, representation is a very general relationship that expresses similarities between objects. Roughly speaking, a collection Y of mathematical objects may be said to represent another collection X of objects, provided that the properties and relationships existing among the representing objects yi conform in some consistent way to those existing among the corresponding represented objects xi.
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Bipartite graph
In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint sets U and V such that every edge connects a vertex in U to one in V; that is, U and V are independent sets. Equivalently, a bipartite graph is a graph that does not contain any odd-length cycles.
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Matching (graph theory)
In the mathematical discipline of graph theory, a matching or independent edge set in a graph is a set of edges without common vertices. It may also be an entire graph consisting of edges without common vertices. Covering-packing dualities Covering problems Packing problems Minimum set cover Maximum set packing Minimum vertex cover Maximum matching Minimum edge cover Maximum independent set
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Combinatorics
Combinatorics is a branch of mathematics concerning the study of finite or countable discrete structures. Aspects of combinatorics include counting the structures of a given kind and size, deciding when certain criteria can be met, and constructing and analyzing objects meeting the criteria, finding "largest", "smallest", or "optimal" objects, and studying combinatorial structures arising in an algebraic context, or applying algebraic techniques to combinatorial problems.
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Data structure
In computer science, a data structure is a particular way of storing and organizing data in a computer so that it can be used efficiently. Different kinds of data structures are suited to different kinds of applications, and some are highly specialized to specific tasks. For example, B-trees are particularly well-suited for implementation of databases, while compiler implementations usually use hash tables to look up identifiers.
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