Improved bounds on the problem of time-space trade-off in the pebble game

Abstract

Every family of graphs Gn with n nodes and bounded in-degree can be pebbled with o(n) pebbles in time o(n 1+c) for all c≫0. There is a family of graphs Gn such that pebbling Gn with O(n/log n) pebbles requires ω(n(log n)k) moves for all k. The n-node jellyfish-graph as defined in (1) can be pebbled with O((log n)2) pebbles and O(n) moves.