A note on many-to-many matchings and stable allocations

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

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...

a note on groups with many locally supersoluble subgroups

it is proved here that if $g$ is a locally graded group satisfying the minimal condition on subgroups which are not locally supersoluble, then $g$ is either locally supersoluble or a vcernikov group. the same conclusion holds for locally finite groups satisfying the weak minimal condition on non-(locally supersoluble) subgroups. as a consequence, it is shown that any infinite locally graded gro...

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 ...