3 research outputs found
Partitioned Matching Games for International Kidney Exchange
We introduce partitioned matching games as a suitable model for international
kidney exchange programmes, where in each round the total number of available
kidney transplants needs to be distributed amongst the participating countries
in a "fair" way. A partitioned matching game is defined on a graph
with an edge weighting and a partition . The player set is , and player owns the
vertices in . The value of a coalition is the
maximum weight of a matching in the subgraph of induced by the vertices
owned by the players in . If for all , then we obtain the
classical matching game. Let be the
width of . We prove that checking core non-emptiness is polynomial-time
solvable if but co-NP-hard if . We do this via pinpointing a
relationship with the known class of -matching games and completing the
complexity classification on testing core non-emptiness for -matching games.
With respect to our application, we prove a number of complexity results on
choosing, out of possibly many optimal solutions, one that leads to a kidney
transplant distribution that is as close as possible to some prescribed fair
distribution
Cooperation in Multiorganization Matching
International audienceWe study a problem involving a set of organizations. Each organization has its own pool of clients who either supply or demand one unit of an indivisible product. Knowing the profit induced by each buyer-seller pair, an organization’s task is to conduct such transactions within its database of clients in order to maximize the amount of the transactions. Inter-organizations transactions are allowed: in this situation, two clients from distinct organizations can trade and their organizations share the induced profit. Since maximizing the overall profit leads to unacceptable situations where an organization can be penalized, we study the problem of maximizing the overall profit such that no organization gets less than it can obtain on its own. Complexity results, an approximation algorithm and a matching inapproximation bound are given
Cooperation in multiorganization matching ∗
We study a problem involving a set of organizations. Each organization has its own pool of clients who either supply or demand one unit of an indivisible product. Knowing the profit induced by each buyer/seller pair, an organization’s task is to conduct such transactions within its database of clients in order to maximize the amount of the transactions. Inter-organizations transactions are allowed: in this situation, two clients from distinct organizations can trade and their organizations share the induced profit. Since maximizing the overall profit leads to unacceptable situations where an organization can be penalized, we study the problem of maximizing the overall profit such that no organization gets less than it can obtain on its own. Complexity results, an approximation algorithm and a matching inapproximation bound are given