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A feedback arc set with the fewest possible edges is a minimum feedback arc set and its removal leaves a maximum acyclic subgraph; weighted versions of these optimization problems are also used. If a feedback arc set is minimal, meaning that removing any edge from it produces a subset that is not a feedback arc set, then it has an additional ...
Feedback arc set [2] [3]: GT8 Graph coloring [2] [3]: GT4 Graph homomorphism problem [3]: GT52 Graph partition into subgraphs of specific types (triangles, isomorphic subgraphs, Hamiltonian subgraphs, forests, perfect matchings) are known NP-complete. Partition into cliques is the same problem as coloring the complement of the
The NP-complete problem Minimum feedback arc set reduces to Min-ULR[≥], with exactly one 1 and one -1 in each constraint, and all right-hand sides equal to 1. [ 6 ] Min-ULR[=,>,≥] are polynomial if the number of variables n is constant: they can be solved polynomially using an algorithm of Greer [ 7 ] in time O ( n ⋅ m n / 2 n − 1 ...
The problem of finding a smallest feedback edge set is equivalent to finding a spanning forest, which can be done in polynomial time. The analogous concept in a directed graph is the feedback arc set (FAS) - a set of directed arcs whose removal makes the graph acyclic. Finding a smallest FAS is an NP-hard problem.
Two examples of such algorithms are the Karger–Stein algorithm [1] and the Monte Carlo algorithm for minimum feedback arc set. [2] The name refers to the Monte Carlo casino in the Principality of Monaco, which is well-known around the world as an icon of gambling. The term "Monte Carlo" was first introduced in 1947 by Nicholas Metropolis. [3]
Image credits: Weird And Wonderful Secondhand Finds The BBC reports that, based on the findings by secondhand fashion retailer ThredUp, a whopping 67% of British millennials shop secondhand, while ...
In computational complexity theory, Karp's 21 NP-complete problems are a set of computational problems which are NP-complete.In his 1972 paper, "Reducibility Among Combinatorial Problems", [1] Richard Karp used Stephen Cook's 1971 theorem that the boolean satisfiability problem is NP-complete [2] (also called the Cook-Levin theorem) to show that there is a polynomial time many-one reduction ...
An arc of flowers or paper flowers on an ofrenda display at Colores Mexicanos. Courtesy Alani Vargas Papel picado is a traditional Mexican decoration that uses thin, tissue paper that people cut ...