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1. Optimal Sensor Placement for Kalman Filtering in Stochastically Forced Consensus Networks

   https://doi.org/10.1109/CDC.2018.8619288  

   Ye, Lintao; Roy, Sandip; Sundaram, Shreyas (December 2018, 2018 IEEE Conference on Decision and Control (CDC))

   Given a linear dynamical system affected by noise, we consider the problem of optimally placing sensors (at design-time) subject to certain budget constraints to minimize the trace of the steady-state error covariance of the Kalman filter. Previous work has shown that this problem is NP-hard in general. In this paper, we impose additional structure by considering systems whose dynamics are given by a stochastic matrix corresponding to an underlying consensus network. In the case when there is a single input at one of the nodes in a tree network, we provide an optimal strategy (computed in polynomial-time) to place the sensors over the network. However, we show that when the network has multiple inputs, the optimal sensor placement problem becomes NP-hard. 

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2. Minimum Wireless Charger Placement with Individual Energy Requirement

   https://doi.org/10.1007/978-3-030-64843-5_47  

   Xingjian Ding, Jianxiong Guo (December 2020, Cocoa)

   null (Ed.)

   Supply energy to battery-powered sensor devices by deploying wireless chargers is a promising way to prolong the operation time of wireless sensor networks, and has attracted much attention recently. Existing works focus on maximizing the total received charging power of the network. However, this may face the unbalanced energy allocation problem, which is not beneficial to prolong the operation time of wireless sensor networks. In this paper, we consider the individual energy requirement of each sensor node, and study the problem of minimum charger placement. That is, we focus on finding a strategy for placing wireless chargers from a given candidate location set, such that each sensor node’s energy requirement can be met, meanwhile the total number of used chargers can be minimized. We show that the problem to be solved is NP-hard, and present two approximation algorithms which are based on the greedy scheme and relax rounding scheme, respectively. We prove that both of the two algorithms have performance guarantees. Finally, we validate the performance of our algorithms by performing extensive numerical simulations. Simulation results show the effectiveness of our proposed algorithms 

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3. Jointly Optimal Routing and Caching for Arbitrary Network Topologies

   https://doi.org/10.1109/JSAC.2018.2844981  

   Ioannidis, Stratis; Yeh, Edmund (June 2018, IEEE Journal on Selected Areas in Communications)

   We study a problem of minimizing routing costs by jointly optimizing caching and routing decisions over an arbitrary network topology. We cast this as an equivalent caching gain maximization problem, and consider both source routing and hop-by-hop routing settings. The respective offline problems are NP-hard. Nevertheless, we show that there exist polynomial time approximation algorithms producing solutions within a constant approximation from the optimal. We also produce distributed, adaptive algorithms with the same approximation guarantees. We simulate our adaptive algorithms over a broad array of different topologies. Our algorithms reduce routing costs by several orders of magnitude compared to prior art, including algorithms optimizing caching under fixed routing. 

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4. On Approximability of 𝓁₂² Min-Sum Clustering

   https://doi.org/10.4230/lipics.socg.2025.62  

   S, Karthik C; Lee, Euiwoong; Rabani, Yuval; Schwiegelshohn, Chris; Zhou, Samson (January 2025, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)

   Aichholzer, Oswin; Wang, Haitao (Ed.)

   The 𝓁₂² min-sum k-clustering problem is to partition an input set into clusters C_1,…,C_k to minimize ∑_{i=1}^k ∑_{p,q ∈ C_i} ‖p-q‖₂². Although 𝓁₂² min-sum k-clustering is NP-hard, it is not known whether it is NP-hard to approximate 𝓁₂² min-sum k-clustering beyond a certain factor. In this paper, we give the first hardness-of-approximation result for the 𝓁₂² min-sum k-clustering problem. We show that it is NP-hard to approximate the objective to a factor better than 1.056 and moreover, assuming a balanced variant of the Johnson Coverage Hypothesis, it is NP-hard to approximate the objective to a factor better than 1.327. We then complement our hardness result by giving a fast PTAS for 𝓁₂² min-sum k-clustering. Specifically, our algorithm runs in time O(n^{1+o(1)}d⋅ 2^{(k/ε)^O(1)}), which is the first nearly linear time algorithm for this problem. We also consider a learning-augmented setting, where the algorithm has access to an oracle that outputs a label i ∈ [k] for input point, thereby implicitly partitioning the input dataset into k clusters that induce an approximately optimal solution, up to some amount of adversarial error α ∈ [0,1/2). We give a polynomial-time algorithm that outputs a (1+γα)/(1-α)²-approximation to 𝓁₂² min-sum k-clustering, for a fixed constant γ > 0. 

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5. Current Flow Group Closeness Centrality for Complex Networks?

   https://doi.org/10.1145/3308558.3313490  

   Li, Huan; Peng, Richard; Shan, Liren; Yi, Yuhao; Zhang, Zhongzhi (June 2019, The World Wide Web Conference, WWW 2019, San Francisco, CA, USA, May 13-17, 2019)

   Current flow closeness centrality (CFCC) has a better discriminating ability than the ordinary closeness centrality based on shortest paths. In this paper, we extend this notion to a group of vertices in a weighted graph, and then study the problem of finding a subset S of k vertices to maximize its CFCC C(S), both theoretically and experimentally. We show that the problem is NP-hard, but propose two greedy algorithms for minimizing the reciprocal of C(S) with provable guarantees using the monotoncity and supermodularity. The first is a deterministic algorithm with an approximation factor (1−kk−1⋅1e) and cubic running time; while the second is a randomized algorithm with a (1−kk−1⋅1e−ϵ)-approximation and nearly-linear running time for any ϵ>0. Extensive experiments on model and real networks demonstrate that our algorithms are effective and efficient, with the second algorithm being scalable to massive networks with more than a million vertices. 

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