5 research outputs found
Adjacency on the constrained assignment problem
AbstractLet Qc,r be the integer hull of the intersection of the assignment polytope with a given hyper-plane H = {x = (xij) ϵ Rn × n: ∑ni = 1 ∑nj = 1 cijxij = r}. We show that the problem of checking whether two given extreme points of Qc,r are nonadjacent on Qc,r is solvable in O(n5) time if c = (cij) is a 0–1 matrix, and that it is NP-Complete if c is a general integer matrix
Vertex adjacencies in the set covering polyhedron
We describe the adjacency of vertices of the (unbounded version of the) set
covering polyhedron, in a similar way to the description given by Chvatal for
the stable set polytope. We find a sufficient condition for adjacency, and
characterize it with similar conditions in the case where the underlying matrix
is row circular. We apply our findings to show a new infinite family of
minimally nonideal matrices.Comment: Minor revision, 22 pages, 3 figure
Shortest Reconfiguration of Perfect Matchings via Alternating Cycles
Motivated by adjacency in perfect matching polytopes, we study the shortest reconfiguration problem of perfect matchings via alternating cycles. Namely, we want to find a shortest sequence of perfect matchings which transforms one given perfect matching to another given perfect matching such that the symmetric difference of each pair of consecutive perfect matchings is a single cycle. The problem is equivalent to the combinatorial shortest path problem in perfect matching polytopes. We prove that the problem is NP-hard even when a given graph is planar or bipartite, but it can be solved in polynomial time when the graph is outerplanar
Adjacency on the constrained assignment problem
http://deepblue.lib.umich.edu/bitstream/2027.42/3205/5/ban3145.0001.001.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/3205/4/ban3145.0001.001.tx