Tessellated Distributed Computing

The work considers the N-server distributed computing scenario with K users requesting functions that are linearly-decomposable over an arbitrary basis of L real (potentially non-linear) subfunctions. In our problem, the aim is for each user to receive their function outputs, allowing for reduced reconstruction error (distortion), reduced computing cost (; the fraction of subfunctions each server must compute), and reduced communication cost (; the fraction of users each server must connect to). For any given set of K requested functions -- which is here represented by a coefficient matrix F R^K L -- our problem is made equivalent to the open problem of sparse matrix factorization that seeks -- for a given parameter T, representing the number of shots for each server -- to minimize the reconstruction distortion 1KL\| F - DE\|²₅ overall -sparse and -sparse matrices D R^K NT and E R^NT L. With these matrices respectively defining which servers compute each subfunction, and which users connect to each server, we here design our D, E by designing tessellated-based and SVD-based fixed support matrix factorization methods that first split F into properly sized and carefully positioned submatrices, which we then approximate and then decompose into properly designed submatrices of D and E.