A Parallel Approach for Embedding Large Pyramids into Smaller Hypercubes with Load Balancing

[[abstract]]With dilation 2, congestion 2, expansion 3/2, and load 1, this short paper first presents a parallel method for embedding a pyramid with height n, P(subscript n), for n≥2, into a (2n-1)-dimensional hypercube, H(subscript 2n-1), in O(n) time. With dilation 2, congestion 2(superscript n-t)+3(or 2(superscript n-t+1)+2), and load [2(superscript 2n-k)/3] when 0≤k=2t (or k=2t-1)≤2n-2, our proposed parallel method is further extended to map P(subscript n) into H(subscript k) with load balancing in O(k) time