PHORMA: Perfectly Hashed Order Restricted Multidimensional Array

TL;DR

This paper introduces PHORMA, a data structure that efficiently creates perfect hash functions for complex order-restricted multidimensional arrays, enabling fast access and additional computations.

Contribution

It presents a novel construction method for perfect hashing of general order-restricted arrays using digraphs, extending previous approaches.

Findings

Constructs a digraph G(a,B) for perfect hashing

Ensures a 1-1 correspondence between paths and array elements

Enables efficient computational tasks on the array structure

Abstract

In this paper we propose a simple and efficient strategy to obtain a data structure generator to accomplish a perfect hash of quite general order restricted multidimensional arrays named {\em phormas}. The constructor of such objects gets two parameters as input: an n-vector a of non negative integers and a boolean function B on the types of order restrictions on the coordinates of the valid n-vectors bounded by a. At compiler time, the phorma constructor builds, from the pair a,B, a digraph G(a,B) with a single source s and a single sink t such that the st-paths are in 1-1 correspondence with the members of the B-restricted a-bounded array A(a,B). Besides perfectly hashing A(a,B), G(a,B) is an instance of an NW-family. This permits other useful computational tasks on it.