scholarly journals Lower bounds for external memory integer sorting via network coding

2020 ◽  
Vol 63 (10) ◽  
pp. 97-105
Author(s):  
Alireza Farhadi ◽  
Mohammad Taghi Hajiaghayi ◽  
Kasper Green Larsen ◽  
Elaine Shi
Keyword(s):  
Network Coding ◽  
Lower Bounds ◽  
External Memory ◽  
Integer Sorting

scholarly journals Lower Bounds for External Memory Integer Sorting via Network Coding

2021 ◽  
pp. STOC19-87-STOC19-111
Author(s):  
Alireza Farhadi ◽  
MohammadTaghi Hajiaghayi ◽  
Kasper Green Larsen ◽  
Elaine Shi
Keyword(s):  
Network Coding ◽  
Lower Bounds ◽  
External Memory ◽  
Integer Sorting

Lower bounds for processing data with few random accesses to external memory

2009 ◽  
Vol 56 (3) ◽  
pp. 1-58 ◽  
Author(s):  
Martin Grohe ◽  
André Hernich ◽  
Nicole Schweikardt
Keyword(s):  
Lower Bounds ◽  
External Memory ◽  
Processing Data

scholarly journals A General Lower Bound on the I/O-Complexity of Comparison-based Algorithms

1992 ◽  
Vol 21 (407) ◽  
Author(s):  
Lars Arge ◽  
Mikael Knudsen ◽  
Kirsten Larsen
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
External Memory ◽  
Optimal Algorithms ◽  
Internal Memory

We show a relationship between the number of comparisons and the number of I/O operations needed to solve a given problem. We work in a model, where the permitted operations are l/O-operations and comparisons of two records in internal memory. An I/O- operation swaps <em>B</em> records between external memory and the internal memory (capable of holding <em>M</em> records). An algorithm for this model is called an I/O-algorithm. The main result of this paper is the following: Given an I/O-algorithm that solves an n-record problem P_n using I/O(bar{x}) I/O's on the input bar{x}, there exists an ordinary comparison algorithm that uses no more than <em>n</em> logB + I/O(bar{x}) € T_{merge}(M-B, B) comparisons on input bar{x}. T_{merge}(n, m) denotes the number of comparisons needed to merge two sorted lists of size n and m, respectively. We use the result to show lower bounds on the number of I/O-operations needed to solve the problems of sorting, removing duplicates from a multiset and determining the mode (the most frequently occurring element in a multiset). Aggarwal and Vitter have shown that the sorting bound is tight. We show the same result for the two other problems, by providing optimal algorithms.

scholarly journals Lower Bounds on the Maximum Energy Benefit of Network Coding for Wireless Multiple Unicast

2010 ◽  
Vol 2010 (1) ◽  
Author(s):  
Jasper Goseling ◽  
Ryutaroh Matsumoto ◽  
Tomohiko Uyematsu ◽  
Jos H. Weber
Keyword(s):  
Network Coding ◽  
Lower Bounds ◽  
Maximum Energy

scholarly journals The Guessing Number of Undirected Graphs

10.37236/679 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Demetres Christofides ◽  
Klas Markström
Keyword(s):  
Network Coding ◽  
Chromatic Number ◽  
Lower Bounds ◽  
Perfect Graphs ◽  
Upper And Lower Bounds ◽  
Undirected Graphs ◽  
Fractional Chromatic Number ◽  
Winning Probability ◽  
Optimal Bounds

Riis [Electron. J. Combin., 14(1):R44, 2007] introduced a guessing game for graphs which is equivalent to finding protocols for network coding. In this paper we prove upper and lower bounds for the winning probability of the guessing game on undirected graphs. We find optimal bounds for perfect graphs and minimally imperfect graphs, and present a conjecture relating the exact value for all graphs to the fractional chromatic number.

scholarly journals Tight lower bounds for query processing on streaming and external memory data

2007 ◽  
Vol 380 (1-2) ◽  
pp. 199-217 ◽  
Author(s):  
Martin Grohe ◽  
Christoph Koch ◽  
Nicole Schweikardt
Keyword(s):  
Query Processing ◽  
Lower Bounds ◽  
External Memory
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