12,523 research outputs found
Inapproximability of maximal strip recovery
In comparative genomic, the first step of sequence analysis is usually to
decompose two or more genomes into syntenic blocks that are segments of
homologous chromosomes. For the reliable recovery of syntenic blocks, noise and
ambiguities in the genomic maps need to be removed first. Maximal Strip
Recovery (MSR) is an optimization problem proposed by Zheng, Zhu, and Sankoff
for reliably recovering syntenic blocks from genomic maps in the midst of noise
and ambiguities. Given genomic maps as sequences of gene markers, the
objective of \msr{d} is to find subsequences, one subsequence of each
genomic map, such that the total length of syntenic blocks in these
subsequences is maximized. For any constant , a polynomial-time
2d-approximation for \msr{d} was previously known. In this paper, we show that
for any , \msr{d} is APX-hard, even for the most basic version of the
problem in which all gene markers are distinct and appear in positive
orientation in each genomic map. Moreover, we provide the first explicit lower
bounds on approximating \msr{d} for all . In particular, we show that
\msr{d} is NP-hard to approximate within . From the other
direction, we show that the previous 2d-approximation for \msr{d} can be
optimized into a polynomial-time algorithm even if is not a constant but is
part of the input. We then extend our inapproximability results to several
related problems including \cmsr{d}, \gapmsr{\delta}{d}, and
\gapcmsr{\delta}{d}.Comment: A preliminary version of this paper appeared in two parts in the
Proceedings of the 20th International Symposium on Algorithms and Computation
(ISAAC 2009) and the Proceedings of the 4th International Frontiers of
Algorithmics Workshop (FAW 2010
Readiness of Quantum Optimization Machines for Industrial Applications
There have been multiple attempts to demonstrate that quantum annealing and,
in particular, quantum annealing on quantum annealing machines, has the
potential to outperform current classical optimization algorithms implemented
on CMOS technologies. The benchmarking of these devices has been controversial.
Initially, random spin-glass problems were used, however, these were quickly
shown to be not well suited to detect any quantum speedup. Subsequently,
benchmarking shifted to carefully crafted synthetic problems designed to
highlight the quantum nature of the hardware while (often) ensuring that
classical optimization techniques do not perform well on them. Even worse, to
date a true sign of improved scaling with the number of problem variables
remains elusive when compared to classical optimization techniques. Here, we
analyze the readiness of quantum annealing machines for real-world application
problems. These are typically not random and have an underlying structure that
is hard to capture in synthetic benchmarks, thus posing unexpected challenges
for optimization techniques, both classical and quantum alike. We present a
comprehensive computational scaling analysis of fault diagnosis in digital
circuits, considering architectures beyond D-wave quantum annealers. We find
that the instances generated from real data in multiplier circuits are harder
than other representative random spin-glass benchmarks with a comparable number
of variables. Although our results show that transverse-field quantum annealing
is outperformed by state-of-the-art classical optimization algorithms, these
benchmark instances are hard and small in the size of the input, therefore
representing the first industrial application ideally suited for testing
near-term quantum annealers and other quantum algorithmic strategies for
optimization problems.Comment: 22 pages, 12 figures. Content updated according to Phys. Rev. Applied
versio
The Satisfiability Threshold for a Seemingly Intractable Random Constraint Satisfaction Problem
We determine the exact threshold of satisfiability for random instances of a
particular NP-complete constraint satisfaction problem (CSP). This is the first
random CSP model for which we have determined a precise linear satisfiability
threshold, and for which random instances with density near that threshold
appear to be computationally difficult. More formally, it is the first random
CSP model for which the satisfiability threshold is known and which shares the
following characteristics with random k-SAT for k >= 3. The problem is
NP-complete, the satisfiability threshold occurs when there is a linear number
of clauses, and a uniformly random instance with a linear number of clauses
asymptotically almost surely has exponential resolution complexity.Comment: This is the long version of a paper that will be published in the
SIAM Journal on Discrete Mathematics. This long version includes an appendix
and a computer program. The contents of the paper are unchanged in the latest
version. The format of the arxiv submission was changed so that the computer
program will appear as an ancillary file. Some comments in the computer
program were update
SWATI: Synthesizing Wordlengths Automatically Using Testing and Induction
In this paper, we present an automated technique SWATI: Synthesizing
Wordlengths Automatically Using Testing and Induction, which uses a combination
of Nelder-Mead optimization based testing, and induction from examples to
automatically synthesize optimal fixedpoint implementation of numerical
routines. The design of numerical software is commonly done using
floating-point arithmetic in design-environments such as Matlab. However, these
designs are often implemented using fixed-point arithmetic for speed and
efficiency reasons especially in embedded systems. The fixed-point
implementation reduces implementation cost, provides better performance, and
reduces power consumption. The conversion from floating-point designs to
fixed-point code is subject to two opposing constraints: (i) the word-width of
fixed-point types must be minimized, and (ii) the outputs of the fixed-point
program must be accurate. In this paper, we propose a new solution to this
problem. Our technique takes the floating-point program, specified accuracy and
an implementation cost model and provides the fixed-point program with
specified accuracy and optimal implementation cost. We demonstrate the
effectiveness of our approach on a set of examples from the domain of automated
control, robotics and digital signal processing
Symmetry Breaking for Answer Set Programming
In the context of answer set programming, this work investigates symmetry
detection and symmetry breaking to eliminate symmetric parts of the search
space and, thereby, simplify the solution process. We contribute a reduction of
symmetry detection to a graph automorphism problem which allows to extract
symmetries of a logic program from the symmetries of the constructed coloured
graph. We also propose an encoding of symmetry-breaking constraints in terms of
permutation cycles and use only generators in this process which implicitly
represent symmetries and always with exponential compression. These ideas are
formulated as preprocessing and implemented in a completely automated flow that
first detects symmetries from a given answer set program, adds
symmetry-breaking constraints, and can be applied to any existing answer set
solver. We demonstrate computational impact on benchmarks versus direct
application of the solver.
Furthermore, we explore symmetry breaking for answer set programming in two
domains: first, constraint answer set programming as a novel approach to
represent and solve constraint satisfaction problems, and second, distributed
nonmonotonic multi-context systems. In particular, we formulate a
translation-based approach to constraint answer set solving which allows for
the application of our symmetry detection and symmetry breaking methods. To
compare their performance with a-priori symmetry breaking techniques, we also
contribute a decomposition of the global value precedence constraint that
enforces domain consistency on the original constraint via the unit-propagation
of an answer set solver. We evaluate both options in an empirical analysis. In
the context of distributed nonmonotonic multi-context system, we develop an
algorithm for distributed symmetry detection and also carry over
symmetry-breaking constraints for distributed answer set programming.Comment: Diploma thesis. Vienna University of Technology, August 201
Liquid State Machine with Dendritically Enhanced Readout for Low-power, Neuromorphic VLSI Implementations
In this paper, we describe a new neuro-inspired, hardware-friendly readout
stage for the liquid state machine (LSM), a popular model for reservoir
computing. Compared to the parallel perceptron architecture trained by the
p-delta algorithm, which is the state of the art in terms of performance of
readout stages, our readout architecture and learning algorithm can attain
better performance with significantly less synaptic resources making it
attractive for VLSI implementation. Inspired by the nonlinear properties of
dendrites in biological neurons, our readout stage incorporates neurons having
multiple dendrites with a lumped nonlinearity. The number of synaptic
connections on each branch is significantly lower than the total number of
connections from the liquid neurons and the learning algorithm tries to find
the best 'combination' of input connections on each branch to reduce the error.
Hence, the learning involves network rewiring (NRW) of the readout network
similar to structural plasticity observed in its biological counterparts. We
show that compared to a single perceptron using analog weights, this
architecture for the readout can attain, even by using the same number of
binary valued synapses, up to 3.3 times less error for a two-class spike train
classification problem and 2.4 times less error for an input rate approximation
task. Even with 60 times larger synapses, a group of 60 parallel perceptrons
cannot attain the performance of the proposed dendritically enhanced readout.
An additional advantage of this method for hardware implementations is that the
'choice' of connectivity can be easily implemented exploiting address event
representation (AER) protocols commonly used in current neuromorphic systems
where the connection matrix is stored in memory. Also, due to the use of binary
synapses, our proposed method is more robust against statistical variations.Comment: 14 pages, 19 figures, Journa
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