This paper presents a new approach to minimize node contention while perfor
ming multiple multicast/broadcast on wormhole k-ary n-cube networks with ov
erlapped destination sets. The existing multicast algorithms in the literat
ure deliver poor performance under multiple multicast because these algorit
hms have been designed with only single multicast in mind. The new algorith
ms introduced in this paper do not use any global knowledge about the respe
ctive destination sets of the concurrent multicasts. Instead, only local in
formation and a source-specific partitioning approach are used. For systems
supporting unicast message-passing, a new SPUmesh (Source-Partitioned Umes
h) algorithm is proposed and is shown to be superior than the conventional
Umesh algorithm [2] for multiple multicast. Two different algorithms, SQHL
(Source-Quadrant Hierarchical Leader) and SCHL (Source-Centered Hierarchica
l Leader), are proposed for systems with multidestination message-passing a
nd shown to be superior than the HL scheme [3]. All of these algorithms per
form 1) 5-10 times faster than the existing algorithms under multiple multi
cast and 2) as fast as existing algorithms under single multicast. Furtherm
ore, the SCHL scheme demonstrates that the latency of multiple multicast ca
n, in fact, be reduced as the degree of multicast increases beyond a certai
n number. Thus, these algorithms demonstrate significant potential to be us
ed for designing fast and scalable collective communication libraries on cu
rrent and future generation wormhole systems.