Competitive Paging Algorithms

Q: How does the algorithm perform in a deterministic server problem?

They showed that LRU running with k servers performs within a factor of k/(k - h + 1) of any off-line algorithm with h 5 k servers and that this is the minimum competitive factor that can be achieved.

Q: What is the deterministic algorithm for the k-server problem?

They showed that no deterministic algorithm for the k-server problem can be better than k-competitive, they gave k-competitive algorithms for the case when k = 2 and k = II - 1, and they conjectured that there exists a k-competitive k-server algorithm for any graph.

Q: What is the probability of a server being on a stale vertex?

The adversary is, however, able to maintain a vector p = (pl, p2,. . . , p,) of probabilities, where pi is the probability that vertex i is not covered by a server.

Q: What is the proof of a randomized on-line algorithm?

In that proof, deterministic on-line algorithms B(l), B(2), . . . , B(m) of type (k, n) were given, and the deterministic on-line algorithm A of type (k, n) was constructed to be &)-competitive against B(i) for each i.

Q: What is the cost of the subphase?

If the total expected cost ends up exceeding l/u, then an arbitrary request is made to an unmarked vertex, and the subphase is over.

Q: What did Manasse and et al. show that A is lazy?

During this phase exactly the vertices of S were requested, so since A is lazy, the authors know that at least d’ of A’s servers were outside of S during the entire phase.

Question

1. What are the contributions mentioned in the paper "Competitive paging algorithms" ?

2. What is the competitive factor for a graph that is an isosceles triangle?

3. What is the simplest way to explain the randomized on-line algorithm?

4. What is the competitive factor of the marking algorithm?

Accepted Answer

In this paper, the authors proposed a method for the analysis of the relationship between computer science degrees and their application in the field of artificial intelligence.

Accepted Answer

Karlin et al. [8] have shown that for two servers in a graph that is an isosceles triangle the best competitive factor that can be achieved is a constant that approaches e/(e - 1) z 1.582 as the length of the similar sides go to infinity.

Accepted Answer

A randomized on-line algorithm may be viewed as basing its actions on the request sequence (T presented to it and on an infinite sequence p of independent unbiased random bits.

Accepted Answer

The marking algorithm is strongly competitive (its competitive factor is Hk) if k = n - 1, but it is not strongly competitive if k < n - 1.

Accepted Answer

They showed that LRU running with k servers performs within a factor of k/(k - h + 1) of any off-line algorithm with h 5 k servers and that this is the minimum competitive factor that can be achieved.

Accepted Answer

They showed that no deterministic algorithm for the k-server problem can be better than k-competitive, they gave k-competitive algorithms for the case when k = 2 and k = II - 1, and they conjectured that there exists a k-competitive k-server algorithm for any graph.

Accepted Answer

The adversary is, however, able to maintain a vector p = (pl, p2,. . . , p,) of probabilities, where pi is the probability that vertex i is not covered by a server.

Accepted Answer

In that proof, deterministic on-line algorithms B(l), B(2), . . . , B(m) of type (k, n) were given, and the deterministic on-line algorithm A of type (k, n) was constructed to be &)-competitive against B(i) for each i.

Accepted Answer

If the total expected cost ends up exceeding l/u, then an arbitrary request is made to an unmarked vertex, and the subphase is over.

Accepted Answer

During this phase exactly the vertices of S were requested, so since A is lazy, the authors know that at least d’ of A’s servers were outside of S during the entire phase.

Accepted Answer

Armed with these tools (the marking and the probability vector), the adversary can generate a sequence such that the expected cost of each phase to A is H,,-l, and the cost to the optimum off-line algorithm is 1.

Competitive Paging Algorithms

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Most frequently asked questions

1. What are the contributions mentioned in the paper "Competitive paging algorithms" ?

2. What is the competitive factor for a graph that is an isosceles triangle?

3. What is the simplest way to explain the randomized on-line algorithm?

4. What is the competitive factor of the marking algorithm?

5. How does the algorithm perform in a deterministic server problem?

6. What is the deterministic algorithm for the k-server problem?

7. What is the probability of a server being on a stale vertex?

8. What is the proof of a randomized on-line algorithm?

9. What is the cost of the subphase?

10. What did Manasse and et al. show that A is lazy?

11. What is the cost to the optimum off-line algorithm?

References

Competitive snoopy caching

Competitive algorithms for server problems

Competitive algorithms for on-line problems

Competitive randomized algorithms for non-uniform problems

A strongly competitive randomized paging algorithm

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