Improved Lower Bounds for Coded Caching

Fundamental Limits of Caching: Improved Bounds with Coded Prefetching

We consider a cache network in which a single server is connected to multiple users via a shared error free link. The server has access to a database with N files of equal length F , and serves K users each with a cache memory of MF bits. A novel centralized coded caching scheme is proposed for scenarios with more users than files N ≤ K and cache capacities satisfying 1 K ≤ M ≤ N K . The propos...

Improved Lower Bounds for Shellsort

We give improved lower bounds for Shellsort based on a new and relatively simple proof idea. The lower bounds obtained are both stronger and more general than the previously known bounds. In particular, they hold for nonmonotone increment sequences and adaptive Shellsort algorithms, as well as for some recently proposed variations of Shellsort.

Improved rate for a multi-server coded caching

Multi-server coded caching, which can further reduce the amount of transmission by means of the collaboration among these servers in the wireless network during the peak traffic times, can be seen everywhere in our life. This amount is called rate. The three servers setting (two data servers and one parity check server)is widely used in practice, e.g. redundant array of independent disks-4. Luo...

Some Lower Bounds for Estrada Index

Improved Recombination Lower Bounds for Haplotype Data

Recombination is an important evolutionary mechanism responsible for the genetic diversity in humans and other organisms. Recently, there has been extensive research on understanding the fine scale variation in recombination rates across the human genome using DNA polymorphism data. A combinatorial approach toward this is to estimate the minimum number of recombination events in any history of ...