S. Albers, S. Arora, and S. Khanna, "Page Replacement for General Caching Problems," Proc. 10th Ann. ACM-SIAM Symp. Discrete Algorithms (SODA '99), pp. 31-40, 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and or a fee. STOC 02, May 19 21, 2002, Montreal, Quebec, Canada. Copyright 2002 ACM 1 58113 495 9 02 0005 . 5.00. petitive analysis [6] and extra resource analysis [2, 5, 7, 13, 16, 17, 18, 20], to study several interesting problems related to the design of on line schedulers on di erent VOD systems and give provably e ective solutions for these problems. In a VOD system, a hot video is often requested over a short period of time (say, Friday 7 p.m. to 9 p.m. Due to the large number ....

....video comprises 120 time units. The total bandwidth for serving both clients is reduced from 240 to 121. ness, and Chan et al. 9] improved their result to obtain a 5 competitive scheduler. The second question is closely related to the extra resource analysis of on line algorithms (see, e.g. [2, 5, 7, 13, 16, 17, 18, 20]) As mentioned before, we have an on line scheduler which is 3 competitive for 20 skimming. Our result suggests that by taking advantage of extra resources, there is an online scheduler for 5 skimming which is 1.2375 competitive relative to 20 skimming. Furthermore, suppose we want to determine ....

S. Albers, S. Arora, and S. Khanna. Page replacement for general caching problems. In Proc. 10th ACM-SIAM SODA, pages 31-40, 17-19 Jan. 1999.

....costs can be formulated as an integer program. When sizes are uniform, the LP relaxation admits an integral solution, and hence, a polynomial time solution. When page sizes vary, the o ine problem becomes NP complete [15] but an approximate solution can be obtained by rounding the LP relaxation [9, 1]. interval caching model and the standard caching model for LRU and LFU. Sections 4 and 5 consider the setup where the next request time of the requested page is provided. Section 4 demonstrates our technique in the simple setting where fetching costs and sizes are uniform, and section 5 ....

S. Albers, S. Arora, and S. Khanna. Page replacement for general caching problems. In Proc. 10th ACM-SIAM Symposium on Discrete Algorithms, pages 31-40. ACM-SIAM, 1999.

....variant of the algorithm greedy dual size previously considered in [4, 15] is k Gammah 1 competitive against the optimal strategy with cache size h k. Our proof provides further insights to greedy dual size. We also indicate how the same integer programming formulation has been recently used [11, 1] to obtain approximation algorithms to the NP complete offline problem. 1 Introduction We consider the paging problem where pages have varying sizes and fetching costs. This problem applies to caching at Web servers, proxies, and browsers. The goal is to maintain a cache of total size at most ....

....problem. First we indicate that one can apply the randomized rounding technique of Ragahavan and Thompson [10] to the solution of the linear programming relaxation of the integer program IP k to obtain a relatively good approximate solution. Furthermore, independently of our work, Albers et al. [11] and Bar Noy et al. 1] used the same integer programming formulation to get better approximation algorithms. We shall review these applications of the integer programming formulation IP k in this section. Finally we show how to formulate the generalized caching problem as a minimum cost ....

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Albers S., Arora S., and Khanna S. Page replacement for general caching problems. In Proc. 10th ACM-SIAM Symposium on Discrete Algorithms. ACM-SIAM, 1999. 8

....independent of our work, Phillips et al. 17] also obtained approximation algorithms for this problem via LP rounding. For discrete input they obtain an approximation factor of 1 4 and for continuous input they obtain an approximation factor of 1 6 . We note that the paper of Albers et al. [1] implies a constant factor approximation (where the constant is at least 22) via LP rounding for the special case where each session can be scheduled in precisely one time interval [15] General Caching The general caching problem models situations in which a cache is to be used for pages of ....

....pages in the cache incur no cost. Since the cache size is fixed, loading one page may necessitate evicting another. The goal is thus to find a minimum cost replacement schedule. We consider the offline version of this problem, i.e. the case where the input is given ahead of time. As was shown in [1], the general caching problem can be modeled in our framework. Our algorithm for this problem yields a 4 approximation. Note that since this is a minimization problem the approximation ratio is at least 1. This improves the result of Albers et al. 1] who were only able to achieve an ....

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S. Albers, A. Arora, and S. Khanna, Page replacement for general caching problems, Proc. 10th Annual ACMSIAM Symposium on Discrete Algorithms, pp. 31--40, 1999.

....then we can obtain an online algorithm that is 12K competitive with respect to the optimal o ine interval strategy. 1. 3 Previous Work There has been much work on the classical caching problem in which requests are for arbitrary blocks and we wish to minimize the aggregate number of cache misses [1, 2, 4, 9, 13]. For example, Sleator and Tarjan [13] showed that the LeastRecently Used (LRU) protocol is B competitive (i.e. the number of cache misses is at most B times the number of misses due to the optimal o ine algorithm) However, the problem of caching streaming data in a network has received less ....

S. Albers, S. Arora and S. Khanna. Page replacement for general caching problems. Proceedings of the 10th Annual Symposium on Discrete Algorithms, 31-40, 1999.

....rounding schemes. We apply a number of techniques including the use of cutting planes to enhance randomized rounding and multiple ltering steps to make sure that both the size and access load constraints on the caches are maintained. 1. 1 Previous Work Previous theoretical work on web caching [5, 1, 6] has focussed on online page replacement policies. We di er from these works in that we assume domains are statically cached in certain caches, and we know the steady state access patterns for these domains by di erent users. Our algorithms are therefore o ine, and need to be run only when there ....

S. Albers, S. Arora, and S. Khanna. Page replacement for general caching problems. Proceedings of 10th ACM-SIAM SODA, 1999.

....costs can be formulated as an integer program. When sizes are uniform, the LP relaxation admits an integral solution, and hence, a polynomial time solution. When page sizes vary, the offline problem becomes NP complete [13] but an approximate solution can be obtained by rounding the LP relaxation [8, 1]. This frameworks yields a near optimal algorithm in the more general (and more realistic) IRD caching model. A simple example demonstrates that cached pages with different distribution function are incomparable, even when pages have uniform sizes and fetching costs. In the example, the first ....

S. Albers, S. Arora, and S. Khanna. Page replacement for general caching problems. In Proc. 10th ACM-SIAM Symposium on Discrete Algorithms, pages 31--40. ACM-SIAM, 1999.

....exactly one clip. In Appendix A, we show how to extend the results mentioned above to the case of multiple clips. 1. 3 Previous Work There has been much work on the classical caching problem in which requests are for arbitrary blocks and we wish to minimize the aggregate number of cache misses [1, 2, 4, 9, 13]. For example, Sleator and Tarjan [13] showed that the Least Recently Used (LRU) protocol is B competitive (i.e. the number of cache misses is at most B times the number of misses due to the optimal o ine algorithm) However, the problem of caching streaming data in a network has received less ....

S. Albers, S. Arora and S. Khanna. Page replacement for general caching problems. Proceedings of the 10th Annual Symposium on Discrete Algorithms, 31-40, 1999.

....Web caching is the temporary local storage of WWW pages by a browser for later retrieval. From the user s point of view, the primary benefit of caching is reduced latency, as the time to access locally stored objects is minimal. We adopt the following standard general model of web caching [1, 5, 8, 14]: Web Caching Problem Statement: The browser is given an online sequence S of page requests, where each page p i 2 S has a size s(i) say, in bytes) and an access time t(i) that is required if p i is not cached. If the requested page p i is not in the cache (this is called a cache miss) then the ....

....for Web Caching on depth first tree traversal sequences S of T , the competitive ratio compares A(S) against the optimal offline cost. We will show that the optimal offline cost may be much higher than t(T ) There are three special cases of the caching models that have been studied previously [1, 8]. In the bit model the access time is assumed to equal the size of the page. This model would be appropriate if the pages are large and the delay in the network is small. In the cost model the size of each page is one, while the access times are allowed to be arbitrary. This is an appropriate ....

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S. Albers, S. Arora, and S. Khanna, "Page replacement for general caching problems", ACM/SIAM Symposium on Discrete Algorithms, 31--40, 1999.

....aims at improving performance, whereas other works focus on increasing availability or avoiding accesses to stale data. Broadcast disk paging poses a trade off between the number of page faults and the cost per fault. Similar trade offs exist in a variety of context, as for example, Web caching [7, 35] and hierarchical paging [15] The problem of finding an optimal cyclic schedule is NP hard [12] but it can be solved in polynomial time if ServerDBSize = 2 [11] The square root law has been proposed by several authors [10, 9, 21, 31] The golden ratio algorithm instantiate the rule and gives a ....

Suzanne Albers, Sanjeev Arora, and Sanjeev Khanna. Page replacement for general caching problems. In Proceedings of the Tenth ACM-SIAM Symposium on Discrete Algorithms, 1999. (To appear).

....Landlord is k competitive in the General Model. For the Bit and the Fault Model, Irani presented O(log 2 k) competitive online algorithms and O(log k) approximation offline algorithms. Here k is the ratio of K to the size of the smallest page requested. For the offline problem, Albers et al. [2] gave constant factor approximation algorithms using only a small amount of additional space in fast memory, say O(1) times the largest page size. Note that the largest page size is typically a very small fraction of the total size of the fast memory, say 1 . The approach is to formulate the ....

....total size of the fast memory, say 1 . The approach is to formulate the caching problems as integer linear programs and then solve a relaxation to obtain a fractional optimal solution. The integrality gap of the linear programs is unbounded, but nevertheless one can show the following. Theorem 9. [2] There is a polynomial time algorithm that, given any request sequence, finds a solution of cost c 1 Delta OPTLP , where OPTLP is the cost of the fractional solution (with fast memory K) The solution uses K c 2 Delta S memory, where S is the size of the largest page in the sequence. The values ....

S. Albers, S. Arora and S. Khanna. Page replacement for general caching problems. Proc. 10th Annual ACM-SIAM Symp. on Discrete Algorithms, 31--40, 1999.

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S. Albers, S. Arora, and S. Khanna, "Page Replacement for General Caching Problems," Proc. 10th Ann. ACM-SIAM Symp. Discrete Algorithms (SODA '99), pp. 31-40, 1999.

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