A Tight Deterministic Algorithm for the Submodular Multiple Knapsack Problem

Submodular function maximization has been a central topic in the theoretical computer science community over the last decade. Plenty of well-performing approximation algorithms have been designed for the maximization of (monotone or non-monotone) submodular functions over a variety of constraints. In this paper, we consider the submodular multiple knapsack problem (SMKP), which is the submodular version of the well-studied multiple knapsack problem (MKP). Roughly speaking, the problem asks to maximize a monotone submodular function over multiple bins (knapsacks). Recently, Fairstein et al. (ESA20) presented a tight $(1-1/e-\epsilon)$-approximation randomized algorithm for SMKP. Their algorithm is based on the continuous greedy technique which inherently involves randomness. However, the deterministic algorithm of this problem has not been understood very well previously. In this paper, we present a tight $(1-1/e-\epsilon)$ deterministic algorithm for SMKP. Our algorithm is based on reducing SMKP to an exponential-size submodular maximizaion problem over a special partition matroid which enjoys a tight deterministic algorithm. We develop several techniques to mimic the algorithm, leading to a tight deterministic approximation for SMKP

Simple Deterministic Approximation for Submodular Multiple Knapsack Problem

Submodular maximization has been a central topic in theoretical computer science and combinatorial optimization over the last decades. Plenty of well-performed approximation algorithms have been designed for the problem over a variety of constraints. In this paper, we consider the submodular multiple knapsack problem (SMKP). In SMKP, the profits of each subset of elements are specified by a monotone submodular function. The goal is to find a feasible packing of elements over multiple bins (knapsacks) to maximize the profit. Recently, Fairstein et al. [ESA20] proposed a nearly optimal (1-e^{-1}-?)-approximation algorithm for SMKP. Their algorithm is obtained by combining configuration LP, a grouping technique for bin packing, and the continuous greedy algorithm for submodular maximization. As a result, the algorithm is somewhat sophisticated and inherently randomized. In this paper, we present an arguably simple deterministic combinatorial algorithm for SMKP, which achieves a (1-e^{-1}-?)-approximation ratio. Our algorithm is based on very different ideas compared with Fairstein et al. [ESA20]

Improved Deterministic Algorithms for Non-monotone Submodular Maximization

Submodular maximization is one of the central topics in combinatorial optimization. It has found numerous applications in the real world. In the past decades, a series of algorithms have been proposed for this problem. However, most of the state-of-the-art algorithms are randomized. There remain non-negligible gaps with respect to approximation ratios between deterministic and randomized algorithms in submodular maximization. In this paper, we propose deterministic algorithms with improved approximation ratios for non-monotone submodular maximization. Specifically, for the matroid constraint, we provide a deterministic $0.283-o(1)$ approximation algorithm, while the previous best deterministic algorithm only achieves a $1/4$ approximation ratio. For the knapsack constraint, we provide a deterministic $1/4$ approximation algorithm, while the previous best deterministic algorithm only achieves a $1/6$ approximation ratio. For the linear packing constraints with large widths, we provide a deterministic $1/6-\epsilon$ approximation algorithm. To the best of our knowledge, there is currently no deterministic approximation algorithm for the constraints.Comment: 25 pages; added a new result about the linear packing constraint

Room-Temperature High-Performance H2S Sensor Based on Porous CuO Nanosheets Prepared by Hydrothermal Method

Porous CuO nanosheets were prepared on alumina tubes using a facile hydrothermal method, and their morphology, microstructure, and gas-sensing properties were investigated. The monoclinic CuO nanosheets had an average thickness of 62.5 nm and were embedded with numerous holes with diameters ranging from 5 to 17 nm. The porous CuO nanosheets were used to fabricate gas sensors to detect hydrogen sulfide (H2S) operating at room temperature. The sensor showed a good response sensitivity of 1.25 with respond/recovery times of 234 and 76 s, respectively, when tested with the H2S concentrations as low as 10 ppb. It also showed a remarkably high selectivity to the H2S, but only minor responses to other gases such as SO2, NO, NO2, H2, CO, and C2H5OH. The working principle of the porous CuO nanosheet based sensor to detect the H2S was identified to be the phase transition from semiconducting CuO to a metallic conducting CuS

High precision NH3 sensing using network nano-sheet Co3O4 arrays based sensor at room temperature

Network nano-sheet arrays of Co3O4 for high precision NH3 sensing application were prepared on alumina tube using a facile hydrothermal process without template or surfactant, and their morphology, nanostructures and NH3 gas sensing performance were investigated. The prepared nano-sheet Co3O4 arrays showed a network structure with an average sheet thickness of 39.5 nm. Detailed structural analysis confirmed that the synthesized Co3O4 nano-sheets were consisted of nanoparticles with an average diameter of 20.0 nm. NH3 gas sensor based on these network Co3O4 nano-sheet arrays showed a low detection limit (0.2 ppm), rapid response/recovery time (9 s/134 s for 0.2 ppm NH3), good reproducibility and long-term stability for NH3 detection at room temperature