MATHEMATICAL ENGINEERING TECHNICAL REPORTS An Algorithm for the Problem of Minimum Weight Packing of Arborescences with Matroid Constraints

As a common generalization of previous arborescence packings, Cs. Király and Szigeti [14] introduced the reachability-based matroid-restricted packing of arborescences. That paper gave a characterization when such a packing exists and a polynomial algorithm for the unweighted case. Here we provide a polynomial algorithm for the weighted case. We reduce the problem to the weighted matroid intersection problem by exploiting the underlying intersecting submodular bi-set function.

[1]  Alexander Schrijver,et al.  Combinatorial optimization. Polyhedra and efficiency. , 2003 .

[2]  James G. Oxley,et al.  Matroid theory , 1992 .

[3]  Hazel Perfect,et al.  A generalization of Rado's theorem on independent transversals , 1969, Mathematical Proceedings of the Cambridge Philosophical Society.

[4]  András Frank,et al.  Rooted k-connections in digraphs , 2009, Discret. Appl. Math..

[5]  András Frank,et al.  Packing Arborescences , 2009 .

[6]  Zoltán Szigeti,et al.  Reachability-based matroid-restricted packing of arborescences , 2017 .

[7]  H. Imai.  NETWORK-FLOW ALGORITHMS FOR LOWER-TRUNCATED TRANSVERSAL POLYMATROIDS , 1983 .

[8]  Jack Edmonds,et al.  Matroids and the greedy algorithm , 1971, Math. Program..

[9]  Yusuke Kobayashi,et al.  Covering Intersecting Bi-set Families under Matroid Constraints , 2016, SIAM J. Discret. Math..

[10]  A. Frank.  Connections in Combinatorial Optimization , 2011 .

[11]  Atsushi Takizawa,et al.  Arc-disjoint in-trees in directed graphs , 2008, SODA '08.

[12]  Kazuo Murota,et al.  Matrices and Matroids for Systems Analysis , 2000 .

[13]  D. R. Fulkerson,et al.  On edge-disjoint branchings , 1976, Networks.

[14]  J. Edmonds.  Matroid Intersection , 2022 .

[15]  Shin-ichi Tanigawa,et al.  Rooted-Tree Decompositions with Matroid Constraints and the Infinitesimal Rigidity of Frameworks with Boundaries , 2011, SIAM J. Discret. Math..

[16]  R. Rado.  A THEOREM ON INDEPENDENCE RELATIONS , 1942 .

[17]  藤重 悟.  Submodular functions and optimization , 1991 .