By Jurek Czyzowicz, David Ilcinkas, Arnaud Labourel (auth.), Haim Kaplan (eds.)

ISBN-10: 3642137318

ISBN-13: 9783642137310

This booklet constitutes the court cases of the twelfth overseas Scandinavian Workshop on set of rules conception, held in Bergen, Norway in June 2010.

**Read or Download Algorithm Theory - SWAT 2010: 12th Scandinavian Symposium and Workshops on Algorithm Theory, Bergen, Norway, June 21-23, 2010. Proceedings PDF**

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**Extra resources for Algorithm Theory - SWAT 2010: 12th Scandinavian Symposium and Workshops on Algorithm Theory, Bergen, Norway, June 21-23, 2010. Proceedings**

**Example text**

F [vi ] [vi+1 ] ← 1 5. B[vi+1 ] [vi ] ← d(vi ) 6. for k ← 2, . . , n2 7. for i ← 0, . . , n − 1 8. j ←i+k 9. for l ← i + 1, . . j − 1 10. if vl ∈ F [vi ] ∧ vl ∈ B[vj ] 11. αi ← ∠vi (F [vi ] [vl ] , |F [vi ]| + 1) (= ↑vi (vl , vj ) , cf. proof of Th. 1) 12. αj ← ∠vj (d(vj ) − |B[vj ]| , B[vj ] [vl ]) (= ↑vj (vi , vl ) , cf. proof of Th. 1) 13. αl ← ∠vl (F [vl ] [vj ] , B[vl ] [vi ]) (= vl (vj , vi ) , cf. proof of Th. 1) 14. if αi + αj + αl = π 15. Evis ← Evis ∪ {vi , vj } 16. F [vi ] [vj ] = |F [vi ]| + 1 17.

Let d0 , d1 , . . , dr−1 and d0 , d1 , . . , dr −1 be strictly-regular representations of d and d . The operations cut(d, i) and concatenate(d, d ) can be executed with O(1) digit changes. Assuming without loss of generality that r ≤ r , add(d, d ) can be executed at O(r) worst-case cost including at most r carries. Proof. Consider the two sequences resulting from a cut. The ﬁrst sequence is strictly regular and requires no changes. The second sequence may have a preceding 1∗ 2 block followed by a strictly-regular subsequence.

H}, the sum of digits is between r and h · r; and in the zeroless regular representation, where di ∈ {1, 2, 3} [7], the sum of digits is between r and 2r. Strictly-Regular Number System and Data Structures 29 An important property, essential for designing data structures with exponential size in terms of their rank, is what we call the exponentiality property. Assume si ≥ θi /c and s0 = 1, for ﬁxed real constants θ > 1 and c > 0. A number r−1 system has such property if for each valid sequence i=0 di · si ≥ θr /c − 1 holds.

### Algorithm Theory - SWAT 2010: 12th Scandinavian Symposium and Workshops on Algorithm Theory, Bergen, Norway, June 21-23, 2010. Proceedings by Jurek Czyzowicz, David Ilcinkas, Arnaud Labourel (auth.), Haim Kaplan (eds.)

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