In this paper, we study the non-monotone DR-submodular function maximization over integer lattice. Functions over integer lattice have been defined submodular property that is similar to submodularity of set functions...
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In this paper we consider three problems of searching for disjoint subsets among a finite set of points in an Euclidean space. In all three problems, it is required to maximize the size of the minimal cluster so that ...
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We introduce deterministic perturbation (DP) schemes for the recently proposed random directions stochastic approximation, and propose new first-order and second-order algorithms. In the latter case, these are the fir...
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We introduce deterministic perturbation (DP) schemes for the recently proposed random directions stochastic approximation, and propose new first-order and second-order algorithms. In the latter case, these are the first second-order algorithms to incorporate DPs. We show that the gradient and/or Hessian estimates in the resulting algorithms with DPs are asymptotically unbiased, so that the algorithms are provably convergent. Furthermore, we derive convergence rates to establish the superiority of the first-order and second-order algorithms, for the special case of a convex and quadratic optimization problem, respectively. Numerical experiments are used to validate the theoretical results.
We consider a variant of the art gallery problem where all guards are limited to seeing 180°. Guards that can only see in one direction are called half-guards. We give a polynomial time approximation scheme for v...
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Given n points in d-dimensional space and a parameter z, we study the problem of finding the smallest axis- aligned bounding box that covers at least n - z points and labels the remaining points as outliers. We consid...
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Introduced by Korman, Kutten, and Peleg (PODC 2005), a proof labeling scheme (PLS) is a distributed verification system dedicated to evaluating if a given configured graph satisfies a certain property. It involves a c...
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We propose two solution concepts for matchings under preferences: robustness and near stability. The former strengthens while the latter relaxes the classical definition of stability by Gale and Shapley (1962). Inform...
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We propose two solution concepts for matchings under preferences: robustness and near stability. The former strengthens while the latter relaxes the classical definition of stability by Gale and Shapley (1962). Informally speaking, robustness requires that a matching must be stable in the classical sense, even if the agents slightly change their preferences. Near stability, however, imposes that a matching must become stable (again, in the classical sense) provided the agents are willing to adjust their preferences a bit. Both of our concepts are quantitative;together they provide means for a fine-grained analysis of the stability of matchings. Moreover, our concepts allow the exploration of tradeoffs between stability and other criteria of social optimality, such as the egalitarian cost and the number of unmatched agents. We investigate the computational complexity of finding matchings that implement certain predefined tradeoffs. We provide a polynomial-time algorithm that, given agent preferences, returns a socially optimal robust matching (if it exists), and we prove that finding a socially optimal and nearly stable matching is computationally hard.
Bayesian analysis enables flexible and rigorous definition of statistical model assumptions with well-characterized propagation of uncertainties and resulting inferences for single-shot, repeated, or even cross-platfo...
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Bayesian analysis enables flexible and rigorous definition of statistical model assumptions with well-characterized propagation of uncertainties and resulting inferences for single-shot, repeated, or even cross-platform data. This approach has a strong history of application to a variety of problems in physical sciences ranging from inference of particle mass from multi-source high-energy particle data to analysis of black-hole characteristics from gravitational wave observations. The recent adoption of Bayesian statistics for analysis and design of high-energy density physics (HEDP) and inertial confinement fusion (ICF) experiments has provided invaluable gains in expert understanding and experiment performance. In this Review, we discuss the basic theory and practical application of the Bayesian statistics framework. We highlight a variety of studies from the HEDP and ICF literature, demonstrating the power of this technique. Due to the computational complexity of multi-physics models needed to analyze HEDP and ICF experiments, Bayesian inference is often not computationally tractable. Two sections are devoted to a review of statistical approximations, efficient inference algorithms, and data-driven methods, such as deep-learning and dimensionality reduction, which play a significant role in enabling use of the Bayesian framework. We provide additional discussion of various applications of Bayesian and machine learning methods that appear to be sparse in the HEDP and ICF literature constituting possible next steps for the community. We conclude by highlighting community needs, the resolution of which will improve trust in data-driven methods that have proven critical for accelerating the design and discovery cycle in many application areas. (c) 2023 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http://***/licenses/by/4.0/). https://***/10.1063/5.0128661
We study the graph burning problem and give a polynomial-time approximation scheme (PTAS) for arbitrary graphs of constant treewidth. This significantly extends the previous results, as a PTAS was known only for disjo...
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This letter proposes a robust beamforming (BF) scheme to enhance physical layer security (PLS) of the downlink of a multibeam satellite system in the presence of either uncoordinated or coordinated eavesdroppers (Eves...
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This letter proposes a robust beamforming (BF) scheme to enhance physical layer security (PLS) of the downlink of a multibeam satellite system in the presence of either uncoordinated or coordinated eavesdroppers (Eves). Specifically, with knowing only the approximate locations of the Eves, we aim at maximizing the worst-case achievable secrecy rate (ASR) of the legitimate user (LU), subject to the constraints of per-antenna transmit power and quality of service (QoS) requirement of the LU. Since the optimization problem is non-convex, we first adopt the discretization method to deal with the unknown regions of the Eves and then exploit the log-sum-exp function to approximate the objective function. Afterwards, a BF method joint alternating direction method of multipliers (ADMM) with Dinkelbach iteration is presented to solve this non-convex problem. Finally, simulation results verify that our robust BF algorithm can effectively improve the security of multibeam satellite systems.
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