293 research outputs found
Unconstrained Submodular Maximization with Constant Adaptive Complexity
In this paper, we consider the unconstrained submodular maximization problem.
We propose the first algorithm for this problem that achieves a tight
-approximation guarantee using
adaptive rounds and a linear number of function evaluations. No previously
known algorithm for this problem achieves an approximation ratio better than
using less than rounds of adaptivity, where is the size
of the ground set. Moreover, our algorithm easily extends to the maximization
of a non-negative continuous DR-submodular function subject to a box constraint
and achieves a tight -approximation guarantee for this
problem while keeping the same adaptive and query complexities.Comment: Authors are listed in alphabetical orde
Unconstrained Submodular Maximization with Constant Adaptive Complexity
In this paper, we consider the unconstrained submodular maximization problem.
We propose the first algorithm for this problem that achieves a tight
-approximation guarantee using
adaptive rounds and a linear number of function evaluations. No previously
known algorithm for this problem achieves an approximation ratio better than
using less than rounds of adaptivity, where is the size
of the ground set. Moreover, our algorithm easily extends to the maximization
of a non-negative continuous DR-submodular function subject to a box constraint
and achieves a tight -approximation guarantee for this
problem while keeping the same adaptive and query complexities.Comment: Authors are listed in alphabetical orde
Non-monotone Submodular Maximization with Nearly Optimal Adaptivity and Query Complexity
Submodular maximization is a general optimization problem with a wide range
of applications in machine learning (e.g., active learning, clustering, and
feature selection). In large-scale optimization, the parallel running time of
an algorithm is governed by its adaptivity, which measures the number of
sequential rounds needed if the algorithm can execute polynomially-many
independent oracle queries in parallel. While low adaptivity is ideal, it is
not sufficient for an algorithm to be efficient in practice---there are many
applications of distributed submodular optimization where the number of
function evaluations becomes prohibitively expensive. Motivated by these
applications, we study the adaptivity and query complexity of submodular
maximization. In this paper, we give the first constant-factor approximation
algorithm for maximizing a non-monotone submodular function subject to a
cardinality constraint that runs in adaptive rounds and makes
oracle queries in expectation. In our empirical study, we use
three real-world applications to compare our algorithm with several benchmarks
for non-monotone submodular maximization. The results demonstrate that our
algorithm finds competitive solutions using significantly fewer rounds and
queries.Comment: 12 pages, 8 figure
Submodular memetic approximation for multiobjective parallel test paper generation
Parallel test paper generation is a biobjective distributed resource optimization problem, which aims to generate multiple similarly optimal test papers automatically according to multiple user-specified assessment criteria. Generating high-quality parallel test papers is challenging due to its NP-hardness in both of the collective objective functions. In this paper, we propose a submodular memetic approximation algorithm for solving this problem. The proposed algorithm is an adaptive memetic algorithm (MA), which exploits the submodular property of the collective objective functions to design greedy-based approximation algorithms for enhancing steps of the multiobjective MA. Synergizing the intensification of submodular local search mechanism with the diversification of the population-based submodular crossover operator, our algorithm can jointly optimize the total quality maximization objective and the fairness quality maximization objective. Our MA can achieve provable near-optimal solutions in a huge search space of large datasets in efficient polynomial runtime. Performance results on various datasets have shown that our algorithm has drastically outperformed the current techniques in terms of paper quality and runtime efficiency
Nearly Linear-Time, Parallelizable Algorithms for Non-Monotone Submodular Maximization
We study parallelizable algorithms for maximization of a submodular function,
not necessarily monotone, with respect to a cardinality constraint . We
improve the best approximation factor achieved by an algorithm that has optimal
adaptivity and query complexity, up to logarithmic factors in the size of
the ground set, from to . We provide two
algorithms; the first has approximation ratio , adaptivity , and query complexity , while the second has
approximation ratio , adaptivity , and query
complexity . Heuristic versions of our algorithms are empirically
validated to use a low number of adaptive rounds and total queries while
obtaining solutions with high objective value in comparison with highly
adaptive approximation algorithms.Comment: 24 pages, 2 figure
- …