Publication

A note on order preserving matchings

Thomas Liebling
1989
Journal Articles

Abstract

We study order preserving injections or bipartite matchings from poset V1 to poset V2. When V1 is totally ordered, we give an efficient algorithm for the associated optimization problem and the convex hull of the corresponding characteristic vectors. If V2 is totally ordered and V1 is not, the problem is NP-complete.

Official source

Graph Chat

Chat with Graph Search

Ask any question about EPFL courses, lectures, exercises, research, news, etc. or try the example questions below.

DISCLAIMER: The Graph Chatbot is not programmed to provide explicit or categorical answers to your questions. Rather, it transforms your questions into API requests that are distributed across the various IT services officially administered by EPFL. Its purpose is solely to collect and recommend relevant references to content that you can explore to help you answer your questions.

Thomas Liebling
1989
Journal Articles

Abstract

Official source

Related concepts (32)

Bipartite graph

In the mathematical field of graph theory, a bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets and , that is, every edge connects a vertex in to one in . Vertex sets and are usually called the parts of the graph. Equivalently, a bipartite graph is a graph that does not contain any odd-length cycles. The two sets and may be thought of as a coloring of the graph with two colors: if one colors all nodes in blue, and all nodes in red, each edge has endpoints of differing colors, as is required in the graph coloring problem.

NP-completeness

In computational complexity theory, a problem is NP-complete when: It is a decision problem, meaning that for any input to the problem, the output is either "yes" or "no". When the answer is "yes", this can be demonstrated through the existence of a short (polynomial length) solution. The correctness of each solution can be verified quickly (namely, in polynomial time) and a brute-force search algorithm can find a solution by trying all possible solutions.

Rainbow matching

In the mathematical discipline of graph theory, a rainbow matching in an edge-colored graph is a matching in which all the edges have distinct colors. Given an edge-colored graph G = (V,E), a rainbow matching M in G is a set of pairwise non-adjacent edges, that is, no two edges share a common vertex, such that all the edges in the set have distinct colors. A maximum rainbow matching is a rainbow matching that contains the largest possible number of edges. Rainbow matchings are of particular interest given their connection to transversals of Latin squares.

Related publications (27)

A note on order preserving matchings

Chat with Graph Search

Group-and-cut approach for dynamic programming with Fréchet-distributed quantizers

Efficient Data-Driven and Physics-Informed Machine Learning for Cardiovascular Modeling

Parameterized algorithms for block-structured integer programs with large entries