335 research outputs found
An Optimal Lower Bound for Buffer Management in Multi-Queue Switches
In the online packet buffering problem (also known as the unweighted FIFO
variant of buffer management), we focus on a single network packet switching
device with several input ports and one output port. This device forwards
unit-size, unit-value packets from input ports to the output port. Buffers
attached to input ports may accumulate incoming packets for later transmission;
if they cannot accommodate all incoming packets, their excess is lost. A packet
buffering algorithm has to choose from which buffers to transmit packets in
order to minimize the number of lost packets and thus maximize the throughput.
We present a tight lower bound of e/(e-1) ~ 1.582 on the competitive ratio of
the throughput maximization, which holds even for fractional or randomized
algorithms. This improves the previously best known lower bound of 1.4659 and
matches the performance of the algorithm Random Schedule. Our result
contradicts the claimed performance of the algorithm Random Permutation; we
point out a flaw in its original analysis
A 4/3-competitive randomized algorithm for online scheduling of packets with agreeable deadlines
In 2005 Li et al. gave a phi-competitive deterministic online algorithm for
scheduling of packets with agreeable deadlines with a very interesting
analysis. This is known to be optimal due to a lower bound by Hajek. We claim
that the algorithm by Li et al. can be slightly simplified, while retaining its
competitive ratio. Then we introduce randomness to the modified algorithm and
argue that the competitive ratio against oblivious adversary is at most 4/3.
Note that this still leaves a gap between the best known lower bound of 5/4 by
Chin et al. for randomised algorithms against oblivious adversary.Comment: 11 pages, 3-4 figures; new version due to STACS submissio
A -Competitive Algorithm for Scheduling Packets with Deadlines
In the online packet scheduling problem with deadlines (PacketScheduling, for
short), the goal is to schedule transmissions of packets that arrive over time
in a network switch and need to be sent across a link. Each packet has a
deadline, representing its urgency, and a non-negative weight, that represents
its priority. Only one packet can be transmitted in any time slot, so, if the
system is overloaded, some packets will inevitably miss their deadlines and be
dropped. In this scenario, the natural objective is to compute a transmission
schedule that maximizes the total weight of packets which are successfully
transmitted. The problem is inherently online, with the scheduling decisions
made without the knowledge of future packet arrivals. The central problem
concerning PacketScheduling, that has been a subject of intensive study since
2001, is to determine the optimal competitive ratio of online algorithms,
namely the worst-case ratio between the optimum total weight of a schedule
(computed by an offline algorithm) and the weight of a schedule computed by a
(deterministic) online algorithm.
We solve this open problem by presenting a -competitive online
algorithm for PacketScheduling (where is the golden ratio),
matching the previously established lower bound.Comment: Major revision of the analysis and some other parts of the paper.
Another revision will follo
Run Generation Revisited: What Goes Up May or May Not Come Down
In this paper, we revisit the classic problem of run generation. Run
generation is the first phase of external-memory sorting, where the objective
is to scan through the data, reorder elements using a small buffer of size M ,
and output runs (contiguously sorted chunks of elements) that are as long as
possible.
We develop algorithms for minimizing the total number of runs (or
equivalently, maximizing the average run length) when the runs are allowed to
be sorted or reverse sorted. We study the problem in the online setting, both
with and without resource augmentation, and in the offline setting.
(1) We analyze alternating-up-down replacement selection (runs alternate
between sorted and reverse sorted), which was studied by Knuth as far back as
1963. We show that this simple policy is asymptotically optimal. Specifically,
we show that alternating-up-down replacement selection is 2-competitive and no
deterministic online algorithm can perform better.
(2) We give online algorithms having smaller competitive ratios with resource
augmentation. Specifically, we exhibit a deterministic algorithm that, when
given a buffer of size 4M , is able to match or beat any optimal algorithm
having a buffer of size M . Furthermore, we present a randomized online
algorithm which is 7/4-competitive when given a buffer twice that of the
optimal.
(3) We demonstrate that performance can also be improved with a small amount
of foresight. We give an algorithm, which is 3/2-competitive, with
foreknowledge of the next 3M elements of the input stream. For the extreme case
where all future elements are known, we design a PTAS for computing the optimal
strategy a run generation algorithm must follow.
(4) Finally, we present algorithms tailored for nearly sorted inputs which
are guaranteed to have optimal solutions with sufficiently long runs
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