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When modelling relations between two different classes of objects, bipartite graphs very often arise naturally. For instance, a graph of football players and clubs, with an edge between a player and a club if the player has played for that club, is a natural example of an affiliation network, a type of bipartite graph used in social network analysis.
A vast majority of problems appearing in programming contests are mathematical or logical in nature. Typical such tasks belong to one of the following categories: combinatorics, number theory, graph theory, algorithmic game theory, computational geometry, string analysis, discrete mathematics and data structures. [6]
At the same time, isomorphism for many special classes of graphs can be solved in polynomial time, and in practice graph isomorphism can often be solved efficiently. [ 3 ] [ 4 ] This problem is a special case of the subgraph isomorphism problem , [ 5 ] which asks whether a given graph G contains a subgraph that is isomorphic to another given ...
Interval scheduling is a class of problems in computer science, particularly in the area of algorithm design. The problems consider a set of tasks. The problems consider a set of tasks. Each task is represented by an interval describing the time in which it needs to be processed by some machine (or, equivalently, scheduled on some resource).
Solution of a travelling salesman problem: the black line shows the shortest possible loop that connects every red dot. In the theory of computational complexity, the travelling salesman problem (TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the ...
In graph theory, a tournament is a directed graph with exactly one edge between each two vertices, in one of the two possible directions.Equivalently, a tournament is an orientation of an undirected complete graph.
A valid schedule for the disjunctive graph may be obtained by finding an acyclic orientation of the undirected edges – that is, deciding for each pair of non-simultaneous tasks which is to be first, without introducing any circular dependencies – and then ordering the resulting directed acyclic graph. In particular, suppose that all tasks ...
Some of the local methods assume that the graph admits a perfect matching; if this is not the case, then some of these methods might run forever. [1]: 3 A simple technical way to solve this problem is to extend the input graph to a complete bipartite graph, by adding artificial edges with very large weights. These weights should exceed the ...