2,136 research outputs found
Energy-Efficient Algorithms
We initiate the systematic study of the energy complexity of algorithms (in
addition to time and space complexity) based on Landauer's Principle in
physics, which gives a lower bound on the amount of energy a system must
dissipate if it destroys information. We propose energy-aware variations of
three standard models of computation: circuit RAM, word RAM, and
transdichotomous RAM. On top of these models, we build familiar high-level
primitives such as control logic, memory allocation, and garbage collection
with zero energy complexity and only constant-factor overheads in space and
time complexity, enabling simple expression of energy-efficient algorithms. We
analyze several classic algorithms in our models and develop low-energy
variations: comparison sort, insertion sort, counting sort, breadth-first
search, Bellman-Ford, Floyd-Warshall, matrix all-pairs shortest paths, AVL
trees, binary heaps, and dynamic arrays. We explore the time/space/energy
trade-off and develop several general techniques for analyzing algorithms and
reducing their energy complexity. These results lay a theoretical foundation
for a new field of semi-reversible computing and provide a new framework for
the investigation of algorithms.Comment: 40 pages, 8 pdf figures, full version of work published in ITCS 201
Prospects and limitations of full-text index structures in genome analysis
The combination of incessant advances in sequencing technology producing large amounts of data and innovative bioinformatics approaches, designed to cope with this data flood, has led to new interesting results in the life sciences. Given the magnitude of sequence data to be processed, many bioinformatics tools rely on efficient solutions to a variety of complex string problems. These solutions include fast heuristic algorithms and advanced data structures, generally referred to as index structures. Although the importance of index structures is generally known to the bioinformatics community, the design and potency of these data structures, as well as their properties and limitations, are less understood. Moreover, the last decade has seen a boom in the number of variant index structures featuring complex and diverse memory-time trade-offs. This article brings a comprehensive state-of-the-art overview of the most popular index structures and their recently developed variants. Their features, interrelationships, the trade-offs they impose, but also their practical limitations, are explained and compared
Estimating the cost of generic quantum pre-image attacks on SHA-2 and SHA-3
We investigate the cost of Grover's quantum search algorithm when used in the
context of pre-image attacks on the SHA-2 and SHA-3 families of hash functions.
Our cost model assumes that the attack is run on a surface code based
fault-tolerant quantum computer. Our estimates rely on a time-area metric that
costs the number of logical qubits times the depth of the circuit in units of
surface code cycles. As a surface code cycle involves a significant classical
processing stage, our cost estimates allow for crude, but direct, comparisons
of classical and quantum algorithms.
We exhibit a circuit for a pre-image attack on SHA-256 that is approximately
surface code cycles deep and requires approximately
logical qubits. This yields an overall cost of
logical-qubit-cycles. Likewise we exhibit a SHA3-256 circuit that is
approximately surface code cycles deep and requires approximately
logical qubits for a total cost of, again,
logical-qubit-cycles. Both attacks require on the order of queries in
a quantum black-box model, hence our results suggest that executing these
attacks may be as much as billion times more expensive than one would
expect from the simple query analysis.Comment: Same as the published version to appear in the Selected Areas of
Cryptography (SAC) 2016. Comments are welcome
Improved reversible and quantum circuits for Karatsuba-based integer multiplication
Integer arithmetic is the underpinning of many quantum algorithms, with applications ranging from Shor\u27s algorithm over HHL for matrix inversion to Hamiltonian simulation algorithms. A basic objective is to keep the required resources to implement arithmetic as low as possible. This applies in particular to the number of qubits required in the implementation as for the foreseeable future this number is expected to be small. We present a reversible circuit for integer multiplication that is inspired by Karatsuba\u27s recursive method. The main improvement over circuits that have been previously reported in the literature is an asymptotic reduction of the amount of space required from O(n^1.585) to O(n^1.427). This improvement is obtained in exchange for a small constant increase in the number of operations by a factor less than 2 and a small asymptotic increase in depth for the parallel version. The asymptotic improvement are obtained from analyzing pebble games on complete ternary trees
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