论文信息 - On Greedy and Submodular Matrices

On Greedy and Submodular Matrices

We characterize non-negative greedy matrices, i.e., (0,1)-matrices A such that the problem max{cT x | Ax ≤ b, x ≥ 0} can be solved greedily. We identify so-called submodular matrices as a special subclass of greedy matrices. Finally, we extend the notion of greediness to {-1,0,1}-matrices. We present numerous applications of these concepts.

[1] B. Bollobás. Surveys in Combinatorics , 1979 .

[2] A. Hoffman,et al. Lattice Polyhedra II: Generalization, Constructions and Examples , 1982 .

[3] Alan J. Hoffman. On greedy algorithms for series parallel graphs , 1988, Math. Program..

[4] Ulrich Faigle,et al. A Characterization of Nonnegative Box-Greedy Matrices , 1996, SIAM J. Discret. Math..

[5] Ulrich Faigle,et al. Two-phase greedy algorithms for some classes of combinatorial linear programs , 2008, TALG.

[7] András Frank,et al. Increasing the rooted-connectivity of a digraph by one , 1999, Math. Program..

[8] A. Hoffman,et al. Totally-Balanced and Greedy Matrices , 1985 .

[9] Ulrich Faigle,et al. A ranking model for the greedy algorithm and discrete convexity , 2012, Math. Program..

[10] Ravindra K. Ahuja,et al. Network Flows: Theory, Algorithms, and Applications , 1993 .

[11] A. J. Hoffman,et al. Surveys in combinatorics 1985: On greedy algorithms that succeed , 1985 .

[12] William R. Pulleyblank,et al. On the submodular matrix representation of a digraph , 2002, Theor. Comput. Sci..

[13] D. R. Fulkerson,et al. Maximal Flow Through a Network , 1956 .

[14] K. Weihe. Maximum (s,t)-Flows in Planar Networks in O( , 1997 .