Codes and cryptography
The art of computer programming, volume 3: (2nd ed.) sorting and searching
The art of computer programming, volume 3: (2nd ed.) sorting and searching
Shifting Graphs and Their Applications
Journal of the ACM (JACM)
Lower Bounds on Merging Networks
Journal of the ACM (JACM)
Lower bounds for merging networks
Information and Computation
Theoretical Computer Science
Optimal conclusive sets for comparator networks
Theoretical Computer Science
Optimal conclusive sets for comparator networks
SIROCCO'07 Proceedings of the 14th international conference on Structural information and communication complexity
On Probabilistic Networks for Selection, Merging, and Sorting
Theory of Computing Systems
| Hi-index | 0.01 |
Let M(m,n) be the minimum number of comparatorsneeded in a comparator network that merges m elements x1≤x2≤&cdots;≤xm and n elements y1≤y2≤&cdots;≤yn , where n≥m . Batcher's odd-even merge yields the following upper bound: Mm,n≤1 2m+nlog 2m+on; in particular, Mn,n≤nlog 2n+On. We prove the following lower bound that matches the upper bound above asymptotically as n≥m→∞: Mm,n≥1 2m+nlog 2m-Om; in particular, Mn,n≥nlog 2n-On. Our proof technique extends to give similarily tight lower bounds for the size of monotone Boolean circuits for merging, and for the size of switching networks capable of realizing the set of permutations that arise from merging.