A parallel algorithm for embedding large pyramids into smaller hypercubes with load balancing

Consider a pyramid with n levels and a k-dimensional hypercube, 0⩽k⩽2n-2. The paper presents a parallel algorithm for embedding large pyramids into smaller hypercubes with load balancing. With dilation 4, congestion at most 2^n-k/2+4, and load [2^2n-k /3] when k is even, our algorithm embeds the pyramid into the hypercube, otherwise, with the same dilation and load, it has congestion 2^n-(k+1)/²⁺¹+6 when k is odd. The algorithm can be performed in O(k)-bit time