Diophantine equations with sum of cubes and cube of sum

Hierarchical Prefix Cubes for Range-Sum Queries

A compression method for prefix-sum cubes

On the Edge-Difference and Edge-Sum Chromatic Sum of the Simple Graphs

‎For a coloring $c$ of a graph $G$‎, ‎the edge-difference coloring sum and edge-sum coloring sum with respect to the coloring $c$ are respectively‎ ‎$sum_c D(G)=sum |c(a)-c(b)|$ and $sum_s S(G)=sum (c(a)+c(b))$‎, ‎where the summations are taken over all edges $abin E(G)$‎. ‎The edge-difference chromatic sum‎, ‎denoted by $sum D(G)$‎, ‎and the edge-sum chromatic sum‎, ‎denoted by $sum S(G)$‎, ‎a...

Dynamic Update Cube for Range-sum Queries

A range-sum query is very popular and becomes important in finding trends and in discovering relationships between attributes in diverse database applications. It sums over the selected cells of an OLAP data cube where target cells are decided by the specified query ranges. The direct method to access the data cube itself forces too many cells to be accessed, therefore it incurs a severe overhe...

Subset sum "cubes" and the complexity of primality testing

A Σ3 Boolean circuit has 3 levels of gates. The input level is comprised of OR gates each taking as inputs 2, not necessarily distinct, literals. Each of these OR’s feeds one or more AND gates at the second level. Their outputs form the inputs to a single OR gate at the output level. Using the projection technique of Paturi, Saks, and Zane, it is shown that the smallest Σ3 Boolean circuit testi...