Efficient 1-Space Bounded Hypercube Packing Algorithm

Abstract

A space bounded $$ O(d/\log d)$$ O ( d / log d ) -competitive hypercube packing algorithm with one active bin only is presented. As a starting point we give a simple 1-space bounded hypercube packing algorithm with competitive ratio $$ (3/2)^{d}+O((21/16)^d)$$ ( 3 / 2 ) d + O ( ( 21 / 16 ) d ) , for $$d\ge 3.$$ d ≥ 3 .