Polynomial-time Construction of Optimal Tree-structured Communication Data Layout Descriptions

TL;DR

This paper presents a polynomial-time algorithm for constructing optimal tree-structured data layout descriptions, improving efficiency in communication of noncontiguous data and solving a previously conjectured NP-hard problem.

Contribution

The authors develop a dynamic programming algorithm that constructs optimal tree descriptions of data layouts, refuting the NP-hardness conjecture and extending to more general constructors.

Findings

Algorithm runs in O(n^4) time and O(n^2) space.

Solves MPI datatype reconstruction problem optimally.

Handles additional constructors beyond MPI specifications.

Abstract

We show that the problem of constructing tree-structured descriptions of data layouts that are optimal with respect to space or other criteria from given sequences of displacements, can be solved in polynomial time. The problem is relevant for efficient compiler and library support for communication of noncontiguous data, where tree-structured descriptions with low-degree nodes and small index arrays are beneficial for the communication soft- and hardware. An important example is the Message-Passing Interface (MPI) which has a mechanism for describing arbitrary data layouts as trees using a set of increasingly general constructors. Our algorithm shows that the so-called MPI datatype reconstruction problem by trees with the full set of MPI constructors can be solved optimally in polynomial time, refuting previous conjectures that the problem is NP-hard. Our algorithm can handle further, natural constructors, currently not found in MPI. Our algorithm is based on dynamic programming, and requires the solution of a series of shortest path problems on an incrementally built, directed, acyclic graph. The algorithm runs in $O(n^4)$ time steps and requires $O(n^2)$ space for input displacement sequences of length $n$.