  The Swapped Dragonfly with M routers per group and K global ports per router
is denoted D3(K;M) [1]. It has n=KMM routers and is a partially populated
Dragonfly. A Swapped Dragonfly with K and M restricted is studied in this
paper. There are four cases. matrix product: If K is a perfect square, a matrix
product of size n can be performed in squareroot n rounds. all-to-all exchange:
If K and M have a common factor s, an all-to-all exchange can be performed in
n/s rounds. broadcast: If D3(K,M) is equipped with a synchronized source-vector
header it can perform x broadcast in 3x/M rounds. ascend-descend: If K and M
are powers of 2 an ascend-descend algorithm can be performed at twice the cost
of the algorithm on a Boolean hypercube of size n. In each case the algorithm
on the Swapped Dragonfly is free of link conflicts and is compared with
algorithms on a hypercube as well as on the fully populated Dragonfly. The
results on the Swapped Dragonfly are more applicable than the special cases
because D3(K,M) contains emulations of every Swapped Dragonfly with J less than
equal to K and/or L less than or equal to M.
  Keywords: Swapped Interconnection Network, Matrix Product, All-to-all,
Universal Exchange, Boolean Hypercube, Ascend-descend algorithm, Broad- cast,
Edge-disjoint spanning tree.
  References [1] R. Draper. The Swapped Dragonfly , ArXiv for Computer
Science:2202.01843. 1
