Algorithms for the partial inverse matroid problem in which weights can only be increased

In a partial inverse combinatorial problem, given a partial solution, the goal is to modify data as small as possible such that there exists an optimal solution containing the given partial solution. In this paper, we study a constraint version of the partial inverse matroid problem in which the weight can only be increased. Two polynomial time algorithms are presented for this problem.

[1]  Elisabeth Gassner.  The partial inverse minimum cut problem with L 1-norm is strongly NP-hard , 2010, RAIRO Oper. Res..

[2]  Panos M. Pardalos,et al.  Encyclopedia of Optimization , 2006 .

[3]  Ravindra K. Ahuja,et al.  Inverse Optimization , 2001, Oper. Res..

[4]  T. Moser.  Shortest path calculation of seismic rays , 1991 .

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

[6]  Xiaoguang Yang,et al.  Partial inverse assignment problems under l1 norm , 2007, Oper. Res. Lett..

[7]  Toshitsugu Ueda,et al.  Rozkład energii napre{ogonek}żeń resztkowych w strukturach dwuwarstwowych , 2012 .

[8]  Clemens Heuberger,et al.  Inverse Combinatorial Optimization: A Survey on Problems, Methods, and Results , 2004, J. Comb. Optim..

[9]  Yang Xiaoguang.  Robust partial inverse network flow problems , 2001 .

[10]  András Frank,et al.  A Weighted Matroid Intersection Algorithm , 1981, J. Algorithms.

[11]  Xiaoguang Yang,et al.  Inverse sorting problem by minimizing the total weighted number of changes and partial inverse sorting problems , 2007, Comput. Optim. Appl..

[12]  Leonidas S. Pitsoulis,et al.  Topics in Matroid Theory , 2013 .

[13]  Philippe L. Toint,et al.  On an instance of the inverse shortest paths problem , 1992, Math. Program..

[14]  Xiaoguang Yang,et al.  The partial inverse minimum spanning tree problem when weight increase is forbidden , 2008, Eur. J. Oper. Res..

[15]  Elisabeth Gassner.  Selected partial inverse combinatorial optimization problems with forbidden elements , 2009 .

[16]  Marc Demange,et al.  An Introduction to Inverse Combinatorial Problems , 2013 .

[17]  Qin Wang.  Partial Inverse Most Unbalanced Spanning Tree Problem , 2012 .

[18]  Mauro Dell'Amico,et al.  The Base-matroid and Inverse Combinatorial Optimization Problems , 2003, Discret. Appl. Math..

[19]  Xiaoguang Yang,et al.  Complexity of Partial Inverse Assignment Problem and Partial Inverse Cut Problem , 2001, RAIRO Oper. Res..