41,039 research outputs found
Parallel machine scheduling with precedence constraints and setup times
This paper presents different methods for solving parallel machine scheduling
problems with precedence constraints and setup times between the jobs. Limited
discrepancy search methods mixed with local search principles, dominance
conditions and specific lower bounds are proposed. The proposed methods are
evaluated on a set of randomly generated instances and compared with previous
results from the literature and those obtained with an efficient commercial
solver. We conclude that our propositions are quite competitive and our results
even outperform other approaches in most cases
Privacy Against Statistical Inference
We propose a general statistical inference framework to capture the privacy
threat incurred by a user that releases data to a passive but curious
adversary, given utility constraints. We show that applying this general
framework to the setting where the adversary uses the self-information cost
function naturally leads to a non-asymptotic information-theoretic approach for
characterizing the best achievable privacy subject to utility constraints.
Based on these results we introduce two privacy metrics, namely average
information leakage and maximum information leakage. We prove that under both
metrics the resulting design problem of finding the optimal mapping from the
user's data to a privacy-preserving output can be cast as a modified
rate-distortion problem which, in turn, can be formulated as a convex program.
Finally, we compare our framework with differential privacy.Comment: Allerton 2012, 8 page
Optimality Clue for Graph Coloring Problem
In this paper, we present a new approach which qualifies or not a solution
found by a heuristic as a potential optimal solution. Our approach is based on
the following observation: for a minimization problem, the number of admissible
solutions decreases with the value of the objective function. For the Graph
Coloring Problem (GCP), we confirm this observation and present a new way to
prove optimality. This proof is based on the counting of the number of
different k-colorings and the number of independent sets of a given graph G.
Exact solutions counting problems are difficult problems (\#P-complete).
However, we show that, using only randomized heuristics, it is possible to
define an estimation of the upper bound of the number of k-colorings. This
estimate has been calibrated on a large benchmark of graph instances for which
the exact number of optimal k-colorings is known. Our approach, called
optimality clue, build a sample of k-colorings of a given graph by running many
times one randomized heuristic on the same graph instance. We use the
evolutionary algorithm HEAD [Moalic et Gondran, 2018], which is one of the most
efficient heuristic for GCP. Optimality clue matches with the standard
definition of optimality on a wide number of instances of DIMACS and RBCII
benchmarks where the optimality is known. Then, we show the clue of optimality
for another set of graph instances. Optimality Metaheuristics Near-optimal
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