# Hsin-Po's Website Math PhD @ UIUC

# Distributed Computation Paper

I have one work on distributed computation.

Abbreviation Title
PlutoCharon20 Parity-Checked Strassen Algorithm

PlutoCharon20 deals with distributed matrix-matrix multiplication (MMM) where the workers might crash or straggle. By MMM we mean that we want to compute $C=AB$, where $A, B$ are huge matrices. By crashing and straggling we mean that some entry multiplication, for instance $A_{12}\times B_{23}$, might be available very late, if at all. This makes the computation slow.

To compensate, one needs to hire more-than-necessary workers and ask them to do redundant computations. A possibility to generate redundancy is to draw random vectors $g, h$ and then ask extra workers to compute $(gA)\times(Bh)$ on top of $A\times B$. Once this is done, the associativity equation $(gA)(Bh)=gCh$ will give you some parity checks that help you recover the missing entries of $C$.

The contribution of PlutoCharon20 is three-fold. One: We obverse that the computation of $A\times B$ can be carried-out by fast matrix multiplication (FMM). This construction is named Pluto codes. Two: Applying Pluto codes recursively, we obtain a code that behaves like tensor product codes. Three: The computation of $(gA)\times(Bh)$, if $g, h$ are matrices, can be carried-out by FMM. This is named Charon construction.