Streamed Graph Drawing and the File Maintenance Problem

TL;DR

This paper presents polynomial-area algorithms for streamed graph drawing that allow minimal coordinate adjustments, connecting the problem to file maintenance algorithms with bulk memory moves.

Contribution

It introduces new algorithms for streamed graph drawing with polynomial area, leveraging a novel connection to the file maintenance problem.

Findings

Polynomial area achievable for streamed graph drawings with small coordinate adjustments

Algorithms for file maintenance problem with bulk memory moves

Applicability to planar trees, tree-maps, and outerplanar graphs

Abstract

In streamed graph drawing, a planar graph, G, is given incrementally as a data stream and a straight-line drawing of G must be updated after each new edge is released. To preserve the mental map, changes to the drawing should be minimized after each update, and Binucci et al.show that exponential area is necessary and sufficient for a number of streamed graph drawings for trees if edges are not allowed to move at all. We show that a number of streamed graph drawings can, in fact, be done with polynomial area, including planar streamed graph drawings of trees, tree-maps, and outerplanar graphs, if we allow for a small number of coordinate movements after each update. Our algorithms involve an interesting connection to a classic algorithmic problem - the file maintenance problem - and we also give new algorithms for this problem in a framework where bulk memory moves are allowed.