Q2. What is the competitive factor for a graph that is an isosceles triangle?
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.
Q3. What is the simplest way to explain the randomized on-line algorithm?
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.
Q4. What is the competitive factor of the marking algorithm?
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.
Q5. 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.
Q6. 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.
Q7. 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.
Q8. 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.
Q9. 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.
Q10. 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.
Q11. What is the cost to the optimum off-line algorithm?
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.