27 research outputs found
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
Stationary Distribution of a Generalized LRU-MRU Content Cache
Many different caching mechanisms have been previously proposed, exploring
different insertion and eviction policies and their performance individually
and as part of caching networks. We obtain a novel closed-form stationary
invariant distribution for a generalization of LRU and MRU caching nodes under
a reference Markov model. Numerical comparisons are made with an "Incremental
Rank Progress" (IRP a.k.a. CLIMB) and random eviction (a.k.a. random
replacement) methods under a steady-state Zipf popularity distribution. The
range of cache hit probabilities is smaller under MRU and larger under IRP
compared to LRU. We conclude with the invariant distribution for a special case
of a random-eviction caching tree-network and associated discussion
Relative Interval Analysis of Paging Algorithms on Access Graphs
Access graphs, which have been used previously in connection with competitive
analysis and relative worst order analysis to model locality of reference in
paging, are considered in connection with relative interval analysis. The
algorithms LRU, FIFO, FWF, and FAR are compared using the path, star, and cycle
access graphs. In this model, some of the expected results are obtained.
However, although LRU is found to be strictly better than FIFO on paths, it has
worse performance on stars, cycles, and complete graphs, in this model. We
solve an open question from [Dorrigiv, Lopez-Ortiz, Munro, 2009], obtaining
tight bounds on the relationship between LRU and FIFO with relative interval
analysis.Comment: IMADA-preprint-c
Truly Online Paging with Locality of Reference
The competitive analysis fails to model locality of reference in the online
paging problem. To deal with it, Borodin et. al. introduced the access graph
model, which attempts to capture the locality of reference. However, the access
graph model has a number of troubling aspects. The access graph has to be known
in advance to the paging algorithm and the memory required to represent the
access graph itself may be very large.
In this paper we present truly online strongly competitive paging algorithms
in the access graph model that do not have any prior information on the access
sequence. We present both deterministic and randomized algorithms. The
algorithms need only O(k log n) bits of memory, where k is the number of page
slots available and n is the size of the virtual address space. I.e.,
asymptotically no more memory than needed to store the virtual address
translation table.
We also observe that our algorithms adapt themselves to temporal changes in
the locality of reference. We model temporal changes in the locality of
reference by extending the access graph model to the so called extended access
graph model, in which many vertices of the graph can correspond to the same
virtual page. We define a measure for the rate of change in the locality of
reference in G denoted by Delta(G). We then show our algorithms remain strongly
competitive as long as Delta(G) >= (1+ epsilon)k, and no truly online algorithm
can be strongly competitive on a class of extended access graphs that includes
all graphs G with Delta(G) >= k- o(k).Comment: 37 pages. Preliminary version appeared in FOCS '9
Online Coded Caching
We consider a basic content distribution scenario consisting of a single
origin server connected through a shared bottleneck link to a number of users
each equipped with a cache of finite memory. The users issue a sequence of
content requests from a set of popular files, and the goal is to operate the
caches as well as the server such that these requests are satisfied with the
minimum number of bits sent over the shared link. Assuming a basic Markov model
for renewing the set of popular files, we characterize approximately the
optimal long-term average rate of the shared link. We further prove that the
optimal online scheme has approximately the same performance as the optimal
offline scheme, in which the cache contents can be updated based on the entire
set of popular files before each new request. To support these theoretical
results, we propose an online coded caching scheme termed coded least-recently
sent (LRS) and simulate it for a demand time series derived from the dataset
made available by Netflix for the Netflix Prize. For this time series, we show
that the proposed coded LRS algorithm significantly outperforms the popular
least-recently used (LRU) caching algorithm.Comment: 15 page