129 research outputs found
Scalable Bicriteria Algorithms for Non-Monotone Submodular Cover
In this paper, we consider the optimization problem \scpl (\scp), which is to
find a minimum cost subset of a ground set such that the value of a
submodular function is above a threshold . In contrast to most
existing work on \scp, it is not assumed that is monotone. Two bicriteria
approximation algorithms are presented for \scp that, for input parameter , give ratio to the optimal cost and ensures
the function is at least . A lower bound shows that
under the value query model shows that no polynomial-time algorithm can ensure
that is larger than . Further, the algorithms presented are
scalable to large data sets, processing the ground set in a stream. Similar
algorithms developed for \scp also work for the related optimization problem of
\smpl (\smp). Finally, the algorithms are demonstrated to be effective in
experiments involving graph cut and data summarization functions
Streaming algorithm for balance gain and cost with cardinality constraint on the integer lattice
Team formation problem is a very important problem in the labor market, and
it is proved to be NP-hard. In this paper, we design an efficient bicriteria
streaming algorithms to construct a balance between gain and cost in a team
formation problem with cardinality constraint on the integer lattice. To solve
this problem, we establish a model for maximizing the difference between a
nonnegative normalized monotone submodule function and a nonnegative linear
function. Further, we discuss the case where the first function of the object
function is --weakly submodular. Combining the lattice binary search
with the threshold method, we present an online algorithm called bicriteria
streaming algorithms. Meanwhile, we give detailed analysis for both of these
models
Streaming Algorithms for Maximizing Monotone Submodular Functions under a Knapsack Constraint
In this paper, we consider the problem of maximizing a monotone submodular function subject to a knapsack constraint in the streaming setting. In particular, the elements arrive sequentially and at any point of time, the algorithm has access only to a small fraction of the data stored in primary memory. For this problem, we propose a (0.363-epsilon)-approximation algorithm, requiring only a single pass through the data; moreover, we propose a (0.4-epsilon)-approximation algorithm requiring a constant number of passes through the data. The required memory space of both algorithms depends only on the size of the knapsack capacity and epsilon
Test Score Algorithms for Budgeted Stochastic Utility Maximization
Motivated by recent developments in designing algorithms based on individual
item scores for solving utility maximization problems, we study the framework
of using test scores, defined as a statistic of observed individual item
performance data, for solving the budgeted stochastic utility maximization
problem. We extend an existing scoring mechanism, namely the replication test
scores, to incorporate heterogeneous item costs as well as item values. We show
that a natural greedy algorithm that selects items solely based on their
replication test scores outputs solutions within a constant factor of the
optimum for a broad class of utility functions. Our algorithms and
approximation guarantees assume that test scores are noisy estimates of certain
expected values with respect to marginal distributions of individual item
values, thus making our algorithms practical and extending previous work that
assumes noiseless estimates. Moreover, we show how our algorithm can be adapted
to the setting where items arrive in a streaming fashion while maintaining the
same approximation guarantee. We present numerical results, using synthetic
data and data sets from the Academia.StackExchange Q&A forum, which show that
our test score algorithm can achieve competitiveness, and in some cases better
performance than a benchmark algorithm that requires access to a value oracle
to evaluate function values
Practical Parallel Algorithms for Non-Monotone Submodular Maximization
Submodular maximization has found extensive applications in various domains
within the field of artificial intelligence, including but not limited to
machine learning, computer vision, and natural language processing. With the
increasing size of datasets in these domains, there is a pressing need to
develop efficient and parallelizable algorithms for submodular maximization.
One measure of the parallelizability of a submodular maximization algorithm is
its adaptive complexity, which indicates the number of sequential rounds where
a polynomial number of queries to the objective function can be executed in
parallel. In this paper, we study the problem of non-monotone submodular
maximization subject to a knapsack constraint, and propose the first
combinatorial algorithm achieving an -approximation under
adaptive complexity, which is \textit{optimal} up to a
factor of . Moreover, we also propose the first
algorithm with both provable approximation ratio and sublinear adaptive
complexity for the problem of non-monotone submodular maximization subject to a
-system constraint. As a by-product, we show that our two algorithms can
also be applied to the special case of submodular maximization subject to a
cardinality constraint, and achieve performance bounds comparable with those of
state-of-the-art algorithms. Finally, the effectiveness of our approach is
demonstrated by extensive experiments on real-world applications.Comment: Part of the contribution appears in AAAI-202
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