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1. Competitive Algorithms for the Online Multiple Knapsack Problem with Application to Electric Vehicle Charging

   https://doi.org/10.1145/3428336  

   Sun, Bo; Zeynali, Ali; Li, Tongxin; Hajiesmaili, Mohammad; Wierman, Adam; Tsang, Danny H.K. (November 2020, Proceedings of the ACM on Measurement and Analysis of Computing Systems)

   null (Ed.)

   We introduce and study a general version of the fractional online knapsack problem with multiple knapsacks, heterogeneous constraints on which items can be assigned to which knapsack, and rate-limiting constraints on the assignment of items to knapsacks. This problem generalizes variations of the knapsack problem and of the one-way trading problem that have previously been treated separately, and additionally finds application to the real-time control of electric vehicle (EV) charging. We introduce a new algorithm that achieves a competitive ratio within an additive factor of one of the best achievable competitive ratios for the general problem and matches or improves upon the best-known competitive ratio for special cases in the knapsack and one-way trading literatures. Moreover, our analysis provides a novel approach to online algorithm design based on an instance-dependent primal-dual analysis that connects the identification of worst-case instances to the design of algorithms. Finally, we illustrate the proposed algorithm via trace-based experiments of EV charging. 

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2. Configuration balancing for stochastic requests

   https://doi.org/10.1007/s10107-024-02132-w  

   Eberle, Franziska; Gupta, Anupam; Megow, Nicole; Moseley, Benjamin; Zhou, Rudy (August 2024, Mathematical Programming)

   Abstract The configuration balancing problem with stochastic requests generalizes well-studied resource allocation problems such as load balancing and virtual circuit routing. There are givenmresources andnrequests; each request has multiple possibleconfigurations, each of which increases the load of each resource by some amount. The goal is to select one configuration for each request to minimize themakespan: the load of the most-loaded resource. In the stochastic setting, the amount by which a configuration increases the resource load is uncertain until the configuration is chosen, but we are given a probability distribution. We develop both offline and online algorithms for configuration balancing with stochastic requests. When the requests are known offline, we give a non-adaptive policy for configuration balancing with stochastic requests that$$O(\frac{\log m}{\log \log m})$$ $O\left(\frac{logm}{loglogm}\right)$-approximates the optimal adaptive policy, which matches a known lower bound for the special case of load balancing on identical machines. When requests arrive online in a list, we give a non-adaptive policy that is$$O(\log m)$$ $O(logm)$competitive. Again, this result is asymptotically tight due to information-theoretic lower bounds for special cases (e.g., for load balancing on unrelated machines). Finally, we show how to leverage adaptivity in the special case of load balancing onrelatedmachines to obtain a constant-factor approximation offline and an$$O(\log \log m)$$ $O(loglogm)$-approximation online. A crucial technical ingredient in all of our results is a new structural characterization of the optimal adaptive policy that allows us to limit the correlations between its decisions. 

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3. Optimal Decision Tree with Noisy Outcomes

   Jia, Su; Nagarajan, Viswanath; Navidi, Fatemeh; Ravi, R (January 2019, Advances in neural information processing systems)

   A fundamental task in active learning involves performing a sequence of tests to identify an unknown hypothesis that is drawn from a known distribution. This problem, known as optimal decision tree induction, has been widely studied for decades and the asymptotically best-possible approximation algorithm has been devised for it. We study a generalization where certain test outcomes are noisy, even in the more general case when the noise is persistent, i.e., repeating the test on the scenario gives the same noisy output, disallowing simple repetition as a way to gain confidence. We design new approximation algorithms for both the non-adaptive setting, where the test sequence must be fixed a-priori, and the adaptive setting where the test sequence depends on the outcomes of prior tests. Previous work in the area assumed at most a constant number of noisy outcomes per test and per scenario and provided approximation ratios that were problem dependent (such as the minimum probability of a hypothesis). Our new approximation algorithms provide guarantees that are nearly best-possible and work for the general case of a large number of noisy outcomes per test or per hypothesis where the performance degrades smoothly with this number. Our results adapt and generalize methods used for submodular ranking and stochastic set cover. We evaluate the performance of our algorithms on two natural applications with noise: toxic chemical identification and active learning of linear classifiers. Despite our logarithmic theoretical approximation guarantees, our methods give solutions with cost very close to the information theoretic minimum, demonstrating the effectiveness of our methods. 

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4. Fast Connectivity Minimization on Large-Scale Networks

   https://doi.org/10.1145/3442342  

   Chen, Chen; Peng, Ruiyue; Ying, Lei; Tong, Hanghang (May 2021, ACM Transactions on Knowledge Discovery from Data)

   null (Ed.)

   The connectivity of networks has been widely studied in many high-impact applications, ranging from immunization, critical infrastructure analysis, social network mining, to bioinformatic system studies. Regardless of the end application domains, connectivity minimization has always been a fundamental task to effectively control the functioning of the underlying system. The combinatorial nature of the connectivity minimization problem imposes an exponential computational complexity to find the optimal solution, which is intractable in large systems. To tackle the computational barrier, greedy algorithm is extensively used to ensure a near-optimal solution by exploiting the diminishing returns property of the problem. Despite the empirical success, the theoretical and algorithmic challenges of the problems still remain wide open. On the theoretical side, the intrinsic hardness and the approximability of the general connectivity minimization problem are still unknown except for a few special cases. On the algorithmic side, existing algorithms are hard to balance between the optimization quality and computational efficiency. In this article, we address the two challenges by (1) proving that the general connectivity minimization problem is NP-hard and is the best approximation ratio for any polynomial algorithms, and (2) proposing the algorithm CONTAIN and its variant CONTAIN + that can well balance optimization effectiveness and computational efficiency for eigen-function based connectivity minimization problems in large networks. 

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5. Quasi-Polynomial Algorithms for Submodular Tree Orienteering and Other Directed Network Design Problems

   https://doi.org/10.1137/1.9781611975994.63  

   Ghuge, Rohan; Nagarajan, Viswanath (January 2020, Proceedings of the Annual ACMSIAM Symposium on Discrete Algorithms)

   We consider the following general network design problem on directed graphs. The input is an asymmetric metric (V, c), root r in V, monotone submodular function f and budget B. The goal is to find an r-rooted arborescence T of cost at most B that maximizes f(T). Our main result is a very simple quasi-polynomial time -approximation algorithm for this problem, where k ≤ |V| is the number of vertices in an optimal solution. To the best of our knowledge, this is the first non-trivial approximation ratio for this problem. As a consequence we obtain an O(log^2 k / loglog k) approximation algorithm for directed (polymatroid) Steiner tree in quasi-polynomial time. We also extend our main result to a setting with additional length bounds at vertices, which leads to improved approximation algorithms for the single-source buy-at-bulk and priority Steiner tree problems. For the usual directed Steiner tree problem, our result matches the best previous approximation ratio, but improves significantly on the running time. For polymatroid Steiner tree and single-source buy-at-bulk, our result improves prior approximation ratios by a logarithmic factor. For directed priority Steiner tree, our result seems to be the first non-trivial approximation ratio. Under certain complexity assumptions, our approximation ratios are best possible (up to constant factors). 

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