7,815 research outputs found
Time-space trade-offs for branching programs
AbstractBranching program depth and the logarithm of branching program complexity are lower bounds on time and space requirements for any reasonable model of sequential computation. In order to gain more insight to the complexity of branching programs and to the problems of time-space trade-offs one considers, on one hand, width-restricted and, on the other hand, depth-restricted branching programs. We present these computation models and the trade-off results already proved. We prove a new result of this type by presenting an effectively defined Boolean function whose complexity in depth-restricted one-time-only branching programs is exponential while its complexity even in width-2 branching programs is polynomial
Hardness of Function Composition for Semantic Read once Branching Programs
In this work, we study time/space trade-offs for function composition. We prove asymptotically optimal lower bounds for function composition in the setting of nondeterministic read once branching programs, for the syntactic model as well as the stronger semantic model of read-once nondeterministic computation. We prove that such branching programs for solving the tree evaluation problem over an alphabet of size k requires size roughly k^{Omega(h)}, i.e space Omega(h log k). Our lower bound nearly matches the natural upper bound which follows the best strategy for black-white pebbling the underlying tree. While previous super-polynomial lower bounds have been proven for read-once nondeterministic branching programs (for both the syntactic as well as the semantic models), we give the first lower bounds for iterated function composition, and in these models our lower bounds are near optimal
Finding the Median (Obliviously) with Bounded Space
We prove that any oblivious algorithm using space to find the median of a
list of integers from requires time . This bound also applies to the problem of determining whether the median
is odd or even. It is nearly optimal since Chan, following Munro and Raman, has
shown that there is a (randomized) selection algorithm using only
registers, each of which can store an input value or -bit counter,
that makes only passes over the input. The bound also implies
a size lower bound for read-once branching programs computing the low order bit
of the median and implies the analog of for length oblivious branching programs
Sublinear Space Algorithms for the Longest Common Substring Problem
Given documents of total length , we consider the problem of finding a
longest string common to at least of the documents. This problem is
known as the \emph{longest common substring (LCS) problem} and has a classic
space and time solution (Weiner [FOCS'73], Hui [CPM'92]).
However, the use of linear space is impractical in many applications. In this
paper we show that for any trade-off parameter , the LCS
problem can be solved in space and time, thus providing
the first smooth deterministic time-space trade-off from constant to linear
space. The result uses a new and very simple algorithm, which computes a
-additive approximation to the LCS in time and
space. We also show a time-space trade-off lower bound for deterministic
branching programs, which implies that any deterministic RAM algorithm solving
the LCS problem on documents from a sufficiently large alphabet in
space must use
time.Comment: Accepted to 22nd European Symposium on Algorithm
Using numerical plant models and phenotypic correlation space to design achievable ideotypes
Numerical plant models can predict the outcome of plant traits modifications
resulting from genetic variations, on plant performance, by simulating
physiological processes and their interaction with the environment.
Optimization methods complement those models to design ideotypes, i.e. ideal
values of a set of plant traits resulting in optimal adaptation for given
combinations of environment and management, mainly through the maximization of
a performance criteria (e.g. yield, light interception). As use of simulation
models gains momentum in plant breeding, numerical experiments must be
carefully engineered to provide accurate and attainable results, rooting them
in biological reality. Here, we propose a multi-objective optimization
formulation that includes a metric of performance, returned by the numerical
model, and a metric of feasibility, accounting for correlations between traits
based on field observations. We applied this approach to two contrasting
models: a process-based crop model of sunflower and a functional-structural
plant model of apple trees. In both cases, the method successfully
characterized key plant traits and identified a continuum of optimal solutions,
ranging from the most feasible to the most efficient. The present study thus
provides successful proof of concept for this enhanced modeling approach, which
identified paths for desirable trait modification, including direction and
intensity.Comment: 25 pages, 5 figures, 2017, Plant, Cell and Environmen
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