609 research outputs found
A New Proposed Cost Model for List Accessing Problem using Buffering
There are many existing well known cost models for the list accessing
problem. The standard cost model developed by Sleator and Tarjan is most widely
used. In this paper, we have made a comprehensive study of the existing cost
models and proposed a new cost model for the list accessing problem. In our
proposed cost model, for calculating the processing cost of request sequence
using a singly linked list, we consider the access cost, matching cost and
replacement cost. The cost of processing a request sequence is the sum of
access cost, matching cost and replacement cost. We have proposed a novel
method for processing the request sequence which does not consider the
rearrangement of the list and uses the concept of buffering, matching, look
ahead and flag bit.Comment: 05 Pages, 2 figure
On-Line Paging against Adversarially Biased Random Inputs
In evaluating an algorithm, worst-case analysis can be overly pessimistic.
Average-case analysis can be overly optimistic. An intermediate approach is to
show that an algorithm does well on a broad class of input distributions.
Koutsoupias and Papadimitriou recently analyzed the least-recently-used (LRU)
paging strategy in this manner, analyzing its performance on an input sequence
generated by a so-called diffuse adversary -- one that must choose each request
probabilitistically so that no page is chosen with probability more than some
fixed epsilon>0. They showed that LRU achieves the optimal competitive ratio
(for deterministic on-line algorithms), but they didn't determine the actual
ratio.
In this paper we estimate the optimal ratios within roughly a factor of two
for both deterministic strategies (e.g. least-recently-used and
first-in-first-out) and randomized strategies. Around the threshold epsilon ~
1/k (where k is the cache size), the optimal ratios are both Theta(ln k). Below
the threshold the ratios tend rapidly to O(1). Above the threshold the ratio is
unchanged for randomized strategies but tends rapidly to Theta(k) for
deterministic ones.
We also give an alternate proof of the optimality of LRU.Comment: Conference version appeared in SODA '98 as "Bounding the Diffuse
Adversary
FIFO anomaly is unbounded
Virtual memory of computers is usually implemented by demand paging. For some
page replacement algorithms the number of page faults may increase as the
number of page frames increases. Belady, Nelson and Shedler constructed
reference strings for which page replacement algorithm FIFO produces near twice
more page faults in a larger memory than in a smaller one. They formulated the
conjecture that 2 is a general bound. We prove that this ratio can be
arbitrarily large
First-Come-First-Served for Online Slot Allocation and Huffman Coding
Can one choose a good Huffman code on the fly, without knowing the underlying
distribution? Online Slot Allocation (OSA) models this and similar problems:
There are n slots, each with a known cost. There are n items. Requests for
items are drawn i.i.d. from a fixed but hidden probability distribution p.
After each request, if the item, i, was not previously requested, then the
algorithm (knowing the slot costs and the requests so far, but not p) must
place the item in some vacant slot j(i). The goal is to minimize the sum, over
the items, of the probability of the item times the cost of its assigned slot.
The optimal offline algorithm is trivial: put the most probable item in the
cheapest slot, the second most probable item in the second cheapest slot, etc.
The optimal online algorithm is First Come First Served (FCFS): put the first
requested item in the cheapest slot, the second (distinct) requested item in
the second cheapest slot, etc. The optimal competitive ratios for any online
algorithm are 1+H(n-1) ~ ln n for general costs and 2 for concave costs. For
logarithmic costs, the ratio is, asymptotically, 1: FCFS gives cost opt + O(log
opt).
For Huffman coding, FCFS yields an online algorithm (one that allocates
codewords on demand, without knowing the underlying probability distribution)
that guarantees asymptotically optimal cost: at most opt + 2 log(1+opt) + 2.Comment: ACM-SIAM Symposium on Discrete Algorithms (SODA) 201
Self-organizing search lists using probabilistic back-pointers
A class of algorithms is given for maintaining self-organizing sequential search lists, where the only permutation applied is to move the accessed record of each search some distance towards the front of the list. During searches, these algorithms retain a back-pointer to a previously probed record in order to determine the destination of the accessed record's eventual move. The back-pointer does not traverse the list, but rather it is advanced occationally to point to the record just probed by the search algorithm. This avoids the cost of a second traversal through a significant portion of the list, which may be a significant savings when each record access may require a new page to be brought into primary memory. Probabilistic functions for deciding when to advance the pointer are presented and analyzed. These functions demonstrate average case complexities of measures such as asymptotic cost and convergence similar to some of the more common list update algorithms in the literature. In cases where the accessed record is moved forward a distance proportional to the distance to the front of the list, the use of these functions may save up to 50% of the time required for permuting the list
On the List Update Problem with Advice
We study the online list update problem under the advice model of
computation. Under this model, an online algorithm receives partial information
about the unknown parts of the input in the form of some bits of advice
generated by a benevolent offline oracle. We show that advice of linear size is
required and sufficient for a deterministic algorithm to achieve an optimal
solution or even a competitive ratio better than . On the other hand, we
show that surprisingly two bits of advice are sufficient to break the lower
bound of on the competitive ratio of deterministic online algorithms and
achieve a deterministic algorithm with a competitive ratio of . In this
upper-bound argument, the bits of advice determine the algorithm with smaller
cost among three classical online algorithms, TIMESTAMP and two members of the
MTF2 family of algorithms. We also show that MTF2 algorithms are
-competitive
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