2,699 research outputs found
The streaming -mismatch problem
We consider the streaming complexity of a fundamental task in approximate
pattern matching: the -mismatch problem. It asks to compute Hamming
distances between a pattern of length and all length- substrings of a
text for which the Hamming distance does not exceed a given threshold . In
our problem formulation, we report not only the Hamming distance but also, on
demand, the full \emph{mismatch information}, that is the list of mismatched
pairs of symbols and their indices. The twin challenges of streaming pattern
matching derive from the need both to achieve small working space and also to
guarantee that every arriving input symbol is processed quickly.
We present a streaming algorithm for the -mismatch problem which uses
bits of space and spends \ourcomplexity time on
each symbol of the input stream, which consists of the pattern followed by the
text. The running time almost matches the classic offline solution and the
space usage is within a logarithmic factor of optimal.
Our new algorithm therefore effectively resolves and also extends an open
problem first posed in FOCS'09. En route to this solution, we also give a
deterministic -bit encoding of all
the alignments with Hamming distance at most of a length- pattern within
a text of length . This secondary result provides an optimal solution to
a natural communication complexity problem which may be of independent
interest.Comment: 27 page
eCMT-SCTP: Improving Performance of Multipath SCTP with Erasure Coding Over Lossy Links
Performance of transport protocols on lossy links is a well-researched topic, however there are only a few proposals making use of the opportunities of erasure coding within the multipath transport protocol context. In this paper, we investigate performance improvements of multipath CMT-SCTP with the novel integration of the on-the-fly erasure code within congestion control and reliability mechanisms. Our contributions include: integration of transport protocol and erasure codes with regards to congestion control; proposal for a variable retransmission delay parameter (aRTX) adjustment; performance evaluation of CMT-SCTP with erasure coding with simulations. We have implemented the explicit congestion notification (ECN) and erasure coding schemes in NS-2, evaluated and demonstrated results of improvement both for application goodput and decline of spurious retransmission. Our results show that we can achieve from 10% to 80% improvements in goodput under lossy network conditions without a significant penalty and minimal overhead due to the encoding-decoding process
Distributed video coding for wireless video sensor networks: a review of the state-of-the-art architectures
Distributed video coding (DVC) is a relatively new video coding architecture originated from two fundamental theorems namely, Slepian–Wolf and Wyner–Ziv. Recent research developments have made DVC attractive for applications in the emerging domain of wireless video sensor networks (WVSNs). This paper reviews the state-of-the-art DVC architectures with a focus on understanding their opportunities and gaps in addressing the operational requirements and application needs of WVSNs
Passive network tomography for erroneous networks: A network coding approach
Passive network tomography uses end-to-end observations of network
communication to characterize the network, for instance to estimate the network
topology and to localize random or adversarial glitches. Under the setting of
linear network coding this work provides a comprehensive study of passive
network tomography in the presence of network (random or adversarial) glitches.
To be concrete, this work is developed along two directions: 1. Tomographic
upper and lower bounds (i.e., the most adverse conditions in each problem
setting under which network tomography is possible, and corresponding schemes
(computationally efficient, if possible) that achieve this performance) are
presented for random linear network coding (RLNC). We consider RLNC designed
with common randomness, i.e., the receiver knows the random code-books all
nodes. (To justify this, we show an upper bound for the problem of topology
estimation in networks using RLNC without common randomness.) In this setting
we present the first set of algorithms that characterize the network topology
exactly. Our algorithm for topology estimation with random network errors has
time complexity that is polynomial in network parameters. For the problem of
network error localization given the topology information, we present the first
computationally tractable algorithm to localize random errors, and prove it is
computationally intractable to localize adversarial errors. 2. New network
coding schemes are designed that improve the tomographic performance of RLNC
while maintaining the desirable low-complexity, throughput-optimal, distributed
linear network coding properties of RLNC. In particular, we design network
codes based on Reed-Solomon codes so that a maximal number of adversarial
errors can be localized in a computationally efficient manner even without the
information of network topology.Comment: 40 pages, under submission for IEEE Trans. on Information Theor
Recognizing well-parenthesized expressions in the streaming model
Motivated by a concrete problem and with the goal of understanding the sense
in which the complexity of streaming algorithms is related to the complexity of
formal languages, we investigate the problem Dyck(s) of checking matching
parentheses, with different types of parenthesis.
We present a one-pass randomized streaming algorithm for Dyck(2) with space
\Order(\sqrt{n}\log n), time per letter \polylog (n), and one-sided error.
We prove that this one-pass algorithm is optimal, up to a \polylog n factor,
even when two-sided error is allowed. For the lower bound, we prove a direct
sum result on hard instances by following the "information cost" approach, but
with a few twists. Indeed, we play a subtle game between public and private
coins. This mixture between public and private coins results from a balancing
act between the direct sum result and a combinatorial lower bound for the base
case.
Surprisingly, the space requirement shrinks drastically if we have access to
the input stream in reverse. We present a two-pass randomized streaming
algorithm for Dyck(2) with space \Order((\log n)^2), time \polylog (n) and
one-sided error, where the second pass is in the reverse direction. Both
algorithms can be extended to Dyck(s) since this problem is reducible to
Dyck(2) for a suitable notion of reduction in the streaming model.Comment: 20 pages, 5 figure
Communication and Streaming Complexity of Approximate Pattern Matching
We consider the approximate pattern matching problem. Given a text T of length 2n and a pattern P of length n, the task is to decide for each prefix T[1, j] of T if it ends with a string that is at the edit distance at most k from P. If this is the case, we must output the edit distance and the corresponding edit operations. We first show the communication complexity of the problem for the case when Alice and Bob both share the pattern and Alice holds the first half of the text and Bob the second half, and for the case when Alice holds the first half of the text, Bob the second half of the text, and Charlie the pattern. We then develop the first sublinear-space streaming algorithm for the problem. The algorithm is randomised with error probability at most 1/poly(n)
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