Cycles to compute the full set of many-to-many stable matchings

An algorithm to compute the full set of many-to-many stable matchings

The paper proposes an algorithm to compute the full set of many-to-many stable matchings when agents have substitutable preferences. The algorithm starts by calculating the two optimal stable matchings using the deferred-acceptance algorithm. Then, it computes each remaining stable matching as the firm-optimal stable matching corresponding to a new preference profile which is obtained after mod...

Single Agents and the Set of Many-to-One Stable Matchings

Some properties of the set of many-to-one stable matchings for firms that have responsive preferences and quotas are not necessarily true when firms' preferences are substitutable. In particular, we provide examples in which firms have substitutable preferences but firms and workers may be ``single'' in one stable matching and matched in another one. We identify a set of axioms on firms' prefer...

Many-to-Many Routing on Trees via Matchings

In this paper we present an extensive study of many-to-many routing on trees under the matching routing model. Our study includes on-line and off-line algorithms. We present an asymptotically optimal on-line algorithm which routes k packets to their destination within d(k 1) + d f dist routing steps, where d is the degree of tree T on which the routing takes place and dist is the maximum distan...

Many-to-Many Routings on Trees via Matchings

Many-to-One Packed Routing via Matchings

In this paper we study the packet routing problem under the matching model proposed by Alon, Chung and Graham 1]. We extend the model to allow more than one packet per origin and destination node. We give tight bounds for the many-to-one routing number for complete graphs, complete bipartite graphs and linear arrays. We also present an eecient algorithm for many-to-one routing on an trees (and ...