Abstract
AbstractWe present various new results on greedoids. We prove a theorem that generalizes an equivalent formulation of Edmonds’ classic matroid polytope theorem to local forest greedoids—a class of greedoids that contains matroids as well as branching greedoids. We also describe an application of this theorem in the field of measuring the reliability of networks by game-theoretical tools. Finally, we prove new results on the optimality of the greedy algorithm on greedoids and correct some mistakes that have been present in the literature for almost 3 decades.
Funder
Országos Tudományos Kutatási Alapprogramok
New Hungary Development Plan
Publisher
Springer Science and Business Media LLC
Subject
General Mathematics,Software
Reference15 articles.
1. Baïou, M., Barahona, F.: Faster algorithms for security games on matroids. Algorithmica 81(3), 1232–1246 (2019)
2. Boyd, E.A.: A Combinatorial Abstraction of the Shortest Path Problem and Its Relationship to Greedoids, CAAM Technical Report, 30 pages (1988)
3. Cunningham, W.H.: Optimal attack and reinforcement of a network. J. ACM (JACM) 32(3), 549–561 (1985)
4. Edmonds, J.: Matroids and the greedy algorithm. Math. Program. 1(1), 127–136 (1971)
5. Helman, P., Moret, B.M.E., Shapiro, H.D.: An exact characterization of greedy structures. SIAM J. Discrete Math. 6, 274–283 (1993)
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