Years and Authors of Summarized Original Work
2003; Mehlhorn, Sanders
Problem Definition
The problem considered here is multiple sequence access via cache memory. Consider the following pattern of memory accesses. k sequences of data, which are stored in disjoint arrays and have a total length of N, are accessed as follows:
for t : = 1 to N do
select a sequence s i  ∈ { 1, … k}
work on the current element of sequence s i
advance sequence s i to the next element.
The aim is to obtain exact (not just asymptotic) closed form upper and lower bounds for this problem. Concurrent accesses to multiple sequences of data are ubiquitous in algorithms. Some examples of algorithms which use this paradigm are distribution sorting, k-way merging, priority queues, permuting, and FFT. This entry summarizes the analyses of this problem in [5, 8].
Caches, Models, and Cache Analysis
Modern computers have hierarchical memory which consists of registers, one or more levels of caches, main memory, and...
Recommended Reading
Bertasi P, Bressan M, Peserico E (2011) Psort, yet another fast stable sorting software. ACM J Exp Algorithmics 16:Article 2.4
Bingmann T, Sanders P (2013) Parallel string sample sort. In: Proceedings of the 21st European symposium on algorithms (ESA’13), Sophia Antipolis. Springer, pp 169–180
Frigo M, Leiserson CE, Prokop H, Ramachandran S (1999) Cache-oblivious algorithms. In: Proceedings of the 40th annual symposium on foundations of computer science (FOCS’99), New York. IEEE Computer Society, Washington, DC, pp 285–297
Ladner RE, Fix JD, LaMarca A (1999) Cache performance analysis of traversals and random accesses. In: Proceedings of the 10th annual ACM-SIAM symposium on discrete algorithms (SODA’99), Baltimore. Society for Industrial and Applied Mathematics, Philadelphia, pp 613–622
Mehlhorn K, Sanders P (2003) Scanning multiple sequences via cache memory. Algorithmica 35:75–93
Rahman N, Raman R (2000) Analysing cache effects in distribution sorting. ACM J Exp Algorithmics 5:Article 14
Rahman N, Raman R (2001) Adapting radix sort to the memory hierarchy. ACM J Exp Algorithmics 6:Article 7
Rahman N, Raman R (2007) Cache analysis of non-uniform distribution sorting algorithms. http://www.citebase.org/abstract?id=oai:arXiv.org:0706.2839. Accessed 13 Aug 2007 Preliminary version in: Proceedings of the 8th annual European symposium on algorithms (ESA’00), Saarbrücken. Lecture notes in computer science, vol 1879. Springer, Berlin/Heidelberg, pp 380–391 (2000)
Sanders P (2000) Fast priority queues for cached memory. ACM J Exp Algorithmics 5:Article 7
Sen S, Chatterjee S (2000) Towards a theory of cache-efficient algorithms. In: Proceedings of the 11th annual ACM-SIAM symposium on discrete algorithms (SODA’00), San Francisco. Society for Industrial and Applied Mathematics, pp 829–838
Vitter JS (2001) External memory algorithms and data structures: dealing with massive data. ACM Comput Surv 33, 209–271
Wassenberg J, Sanders P (2011) Engineering a Multi-core Radix Sort, In: Proceedings of the 17th international conference, Euro-Par (2) 2011, Bordeaux. Springer, pp 160–169
Wickremesinghe R, Arge L, Chase JS, Vitter JS (2002) Efficient sorting using registers and caches. ACM J Exp Algorithmics 7:9
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Rahman, N. (2015). Analyzing Cache Misses. In: Kao, MY. (eds) Encyclopedia of Algorithms. Springer, Boston, MA. https://doi.org/10.1007/978-3-642-27848-8_14-2
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DOI: https://doi.org/10.1007/978-3-642-27848-8_14-2
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