TOWARDS SCALABILITY IN TUPLE SPACES Philipp Obreiter Guntram

TOWARDS SCALABILITY IN TUPLE SPACES Philipp Obreiter, Guntram Gräf Telecooperation Office (Tec. O) University of Karlsruhe

Obreiter/Gräf: Towards Scalability in Tuple Spaces Scalability Five dimensions: • size of tuples • number of tuples in the tuple space • number of considered tuple spaces • throughput of the tuple space • number of clients

Obreiter/Gräf: Towards Scalability in Tuple Spaces Goals Scalable tuple space – without schematic restrictions Procedure: • formalize and classify tuples • analyze former indexing strategies • deduce a new indexing strategy • conceive the architecture and implementation of a scalable tuple space

Obreiter/Gräf: Towards Scalability in Tuple Spaces Hierarchy of fields (F, match. F) F int 1234 string 5678 “Hello“ “World“

Obreiter/Gräf: Towards Scalability in Tuple Spaces Hierarchy of fields F x modulo y fraction x modulo 3 x modulo 5 0 0 1 2 4 1/2 2/4 6/9 4/6 1 3 2

Obreiter/Gräf: Towards Scalability in Tuple Spaces Hierarchy of tuples ( , match ) (int, F) (int, int)) ( F, string) (int, string) (1234, (56, 78)) (1234, string) ( F, “Hello“) (int, “Hello“) (5678, “Hello“)

Obreiter/Gräf: Towards Scalability in Tuple Spaces Distribution model • Set of p servers {1, . . . , p} • Distribution ( W, R) for tuple t – writes to W(t) {1, . . . , p} – reads from R(t) {1, . . . , p} 1 2 3 R condition for correctness match (t 1, t 2) W(t 2) R(t 1) 4 W 5 6

Obreiter/Gräf: Towards Scalability in Tuple Spaces Conceiving a distribution t W(t) t R(t) directly abstract representation W(t) indirectly Abstract representation – uncouples abstraction of tuples and adjustment to p – is an efficient data structure R(t)

Obreiter/Gräf: Towards Scalability in Tuple Spaces Indexing based on hashing (I) (F) (printer, F, F) ( F, 1200 dpi, F) (printer, 1200 dpi, F) P 1 P 2 (scanner, F, F) (scanner, 1200 dpi, F) ( F, 1200 dpi, x. x) P 3 P 4 P 5 S 1 S 3 S 2 S 4 S 5

Obreiter/Gräf: Towards Scalability in Tuple Spaces Indexing based on hashing (II) (F) (printer, F, F) ( F, 1200 dpi, F) (printer, 1200 dpi, F) {1} P 1 {5} P 2 (scanner, F, F) (scanner, 1200 dpi, F) ( F, 1200 dpi, x. x) {6} P 3 {8} P 4 {3} P 5 {12} S 1 {2} S 3 {5} S 2 {7} S 4 {8} S 5

Obreiter/Gräf: Towards Scalability in Tuple Spaces Indexing based on hashing (III) (F) (printer, F, F) ( F, 1200 dpi, F) {3} (printer, 1200 dpi, F) P 1 P 2 (scanner, F, F) {7} (scanner, 1200 dpi, F) ( F, 1200 dpi, x. x) P 3 P 4 P 5 S 1 S 3 S 2 S 4 S 5

Obreiter/Gräf: Towards Scalability in Tuple Spaces Indexing based on hypercubes • Fields: – hierarchical structure intervals instead of points – correctness: match. F(f 1, f 2) F(f 1) • Tuples: – tuple complex multi-dimensional index – induces transformation to hypercubes • Distribution: – Partition hyperspace into tuple domains 1, . . . p – ( , ) permissible with (t) : = {q | q (t) }

Obreiter/Gräf: Towards Scalability in Tuple Spaces disjoint/complete tuple domains x 1 5 T 4 T 6 4 3 T 5 2 T 1 -1 T 3 1 T 2 0 1 2 3 4 5 x 2

Obreiter/Gräf: Towards Scalability in Tuple Spaces disjoint/complete tuple domains x 1 2 5 T 4 1 T 1 -1 T 6 4 3 T 5 2 3 T 3 4 1 0 1 5 T 2 2 3 4 5 x 2

Obreiter/Gräf: Towards Scalability in Tuple Spaces Tree of tuple domains x 2 = 0 x 1 = 2 2 x 1 = 4 x 2 = 3 4 5 3 2

Obreiter/Gräf: Towards Scalability in Tuple Spaces Overlapping/incomplete tuple domains x 1 5 T 4 T 6 4 3 T 5 2 1 T 1 -1 3 T 3 1 2 T 2 0 1 2 3 4 5 x 2

Obreiter/Gräf: Towards Scalability in Tuple Spaces SAT US • • • Implementation of a Scalable Tuple Spaces Management interface Extension to four tiers Built-in standard fields Validated with respect to: – Efficiency of the distribution – Efficiency of adaptive tuple domains

Rate Obreiter/Gräf: Towards Scalability in Tuple Spaces Efficiency of the distribution 1. 8 pruning rate . 6. 4. 2 0 50 100 150 200 250 300 350 400 overhead n 450 500

Obreiter/Gräf: Towards Scalability in Tuple Spaces Questions?