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1. Distributed Graph Diameter Approximation

   https://doi.org/10.3390/a13090216  

   Ceccarello, Matteo; Pietracaprina, Andrea; Pucci, Geppino; Upfal, Eli (September 2020, Algorithms)

   null (Ed.)

   We present an algorithm for approximating the diameter of massive weighted undirected graphs on distributed platforms supporting a MapReduce-like abstraction. In order to be efficient in terms of both time and space, our algorithm is based on a decomposition strategy which partitions the graph into disjoint clusters of bounded radius. Theoretically, our algorithm uses linear space and yields a polylogarithmic approximation guarantee; most importantly, for a large family of graphs, it features a round complexity asymptotically smaller than the one exhibited by a natural approximation algorithm based on the state-of-the-art Δ-stepping SSSP algorithm, which is its only practical, linear-space competitor in the distributed setting. We complement our theoretical findings with a proof-of-concept experimental analysis on large benchmark graphs, which suggests that our algorithm may attain substantial improvements in terms of running time compared to the aforementioned competitor, while featuring, in practice, a similar approximation ratio. 

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2. Adaptive Discretization for Episodic Reinforcement Learning in Metric Spaces

   https://doi.org/10.1145/3410048.3410059  

   Sinclair, Sean R.; Banerjee, Siddhartha; Lee Yu, Christina (July 2020, ACM SIGMETRICS Performance Evaluation Review)

   null (Ed.)

   We present an efficient algorithm for model-free episodic reinforcement learning on large (potentially continuous) state-action spaces. Our algorithm is based on a novel Q-learning policy with adaptive data-driven discretization. The central idea is to maintain a finer partition of the state-action space in regions which are frequently visited in historical trajectories, and have higher payoff estimates. We demonstrate how our adaptive partitions take advantage of the shape of the optimal Q-function and the joint space, without sacrificing the worst-case performance. In particular, we recover the regret guarantees of prior algorithms for continuous state-action spaces, which additionally require either an optimal discretization as input, and/or access to a simulation oracle. Moreover, experiments demonstrate how our algorithm automatically adapts to the underlying structure of the problem, resulting in much better performance compared both to heuristics and Q-learning with uniform discretization. 

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3. Efficient multi-robot coverage of a known environment

   https://doi.org/10.1109/IROS.2017.8206000  

   Karapetyan, Nare; Benson, Kelly; McKinney, Chris; Taslakian, Perouz; Rekleitis, Ioannis (September 2017, IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS))

   This paper addresses the complete area coverage problem of a known environment by multiple-robots. Complete area coverage is the problem of moving an end-effector over all available space while avoiding existing obstacles. In such tasks, using multiple robots can increase the efficiency of the area coverage in terms of minimizing the operational time and increase the robustness in the face of robot attrition. Unfortunately, the problem of finding an optimal solution for such an area coverage problem with multiple robots is known to be NP-complete. In this paper we present two approximation heuristics for solving the multi-robot coverage problem. The first solution presented is a direct extension of an efficient single robot area coverage algorithm, based on an exact cellular decomposition. The second algorithm is a greedy approach that divides the area into equal regions and applies an efficient single-robot coverage algorithm to each region. We present experimental results for two algorithms. Results indicate that our approaches provide good coverage distribution between robots and minimize the workload per robot, meanwhile ensuring complete coverage of the area. 

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4. Machine learning aided optimization for balanced resource allocations in SDM-EONs

   https://doi.org/10.1364/JOCN.481415  

   Petale, Shrinivas; Subramaniam, Suresh (April 2023, Journal of Optical Communications and Networking)

   A fine-grained flexible frequency grid for elastic optical transmission and space division multiplexing in conjunction with spectrally efficient modulations is an excellent solution to the coming capacity crunch. In space division multiplexed elastic optical networks (SDM-EONs), the routing, modulation, core, and spectrum assignment (RMCSA) problem is an important lightpath resource assignment problem. Intercore cross talk (XT) reduces the quality of parallel transmissions on separate cores, and the RMCSA algorithm must ensure that XT requirements are satisfied while optimizing network performance. There is an indirect trade-off between spectrum utilization and XT tolerance; while higher modulations are more spectrum efficient, they are also less tolerant of XT since they permit fewer connections on neighboring cores on the overlapping spectra. Numerous XT-aware RMCSA algorithms restrict the number of litcores, cores on which overlapping spectra are occupied, to guarantee XT constraints are met. In this paper, we present a machine learning (ML) aided threshold optimization strategy that enhances the performance ofanyRMCSA algorithm for any network model. We show that our strategy applied to a few algorithms from the literature improves the bandwidth blocking probability by up to three orders of magnitude. We also present the RMCSA algorithm called spectrum-wastage-avoidance-based resource allocation (SWARM), which is based on the idea of spectrum wastage due to spectrum requirements and XT constraints. We note that SWARM not only outperforms other RMCSA algorithms, but also its ML-optimized variant outperforms other ML-optimized RMCSA algorithms. 

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5. Simulating Markovian Open Quantum Systems Using Higher-Order Series Expansion

   https://doi.org/10.4230/LIPIcs.ICALP.2023.87  

   Li, Xiantao; Wang, Chunhao (January 2023, Leibniz International Proceedings in Informatics (LIPIcs):50th International Colloquium on Automata, Languages, and Programming (ICALP 2023))

   Etessami, Kousha; Feige, Uriel; Puppis, Gabriele (Ed.)

   We present an efficient quantum algorithm for simulating the dynamics of Markovian open quantum systems. The performance of our algorithm is similar to the previous state-of-the-art quantum algorithm, i.e., it scales linearly in evolution time and poly-logarithmically in inverse precision. However, our algorithm is conceptually cleaner, and it only uses simple quantum primitives without compressed encoding. Our approach is based on a novel mathematical treatment of the evolution map, which involves a higher-order series expansion based on Duhamel’s principle and approximating multiple integrals using scaled Gaussian quadrature. Our method easily generalizes to simulating quantum dynamics with time-dependent Lindbladians. Furthermore, our method of approximating multiple integrals using scaled Gaussian quadrature could potentially be used to produce a more efficient approximation of time-ordered integrals, and therefore can simplify existing quantum algorithms for simulating time-dependent Hamiltonians based on a truncated Dyson series. 

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