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PAC Learning with Bandit Feedback: Sharp Sample Complexity in the Realizable Setting Algorithms with Polynomially-Improved Approximation Factors for the $2 \rightarrow q$ Norm, and Applications A computational phase transition for learning-to-sample from Ising models Covering vertices by sequential stars Fermi-Dirac machines as quantizations of neurons A Comprehensive Evaluation of Vertex Elimination Algorithms for Algorithmic Differentiation A Tight Bound on Localization of Electrical Flows Optimal Dimension-Free Sampling for Regularized Classification Reducing the Randomness in Partition Oracles for Bounded Degree Minor-Free Graphs Beyond the Half-Approximation: Fair and Efficient Online Class Matching Efficient Uniform Sampling of Surjections via their Profiles Tractable Maximization of Budgeted Phylogenetic Diversity on Networks Utilizing Node Scanwidth Fairness in Aggregation: Optimal Top-$k$ and Improved Full Ranking Learning-Augmented Online Scheduling with Parsimonious Preemption Entropy Equivalence Testing Lumberjack: Better Differentially Private Random Forests through Heavy Hitter Detection in Trees The Secretary Problem with a Stochastic Precursor Polynomial-Time Robust Multiclass Linear Classification under Gaussian Marginals Efficient Banzhaf-Based Data Valuation for $k$-Nearest Neighbors Classification Block-Sphere Vector Quantization An Approximation Algorithm for Graph Label Selection Iterative Chow Filtering for Learning with Distribution Shift Complexity of Non-Log-Concave Sampling in Fisher Information Stochastic Matching via Local Sparsification Finite Sample Bounds for Learning with Score Matching What is Learnable in Valiant's Theory of the Learnable? Provable Quantization with Randomized Hadamard Transform Min-Max Optimization Requires Exponentially Many Queries Fast and Compact Graph Cuts for the Boykov-Kolmogorov Algorithm A proximal gradient algorithm for composite log-concave sampling
Dynamic Programming Optimization in Line of Sight Networks
Pavan Sangha, Prudence W. H. Wong, Michele Zito · 2018-06-05 · via cs.DS updates on arXiv.org

Line of Sight (LoS) networks were designed to model wireless communication in settings which may contain obstacles restricting node visibility. For fixed positive integer $d$, and positive integer $ω$, a graph $G=(V,E)$ is a ($d$-dimensional) LoS network with range parameter $ω$ if it can be embedded in a cube of side size $n$ of the $d$-dimensional integer grid so that each pair of vertices in $V$ are adjacent if and only if their embedding coordinates differ only in one position and such difference is less than $ω$. In this paper we investigate a dynamic programming (DP) approach which can be used to obtain efficient algorithmic solutions for various combinatorial problems in LoS networks. In particular DP solves the Maximum Independent Set (MIS) problem in LoS networks optimally for any $ω$ on {\em narrow} LoS networks (i.e. networks which can be embedded in a $n \times k \times k \ldots \times k$ region, for some fixed $k$ independent of $n$). In the unrestricted case it has been shown that the MIS problem is NP-hard when $ ω> 2$ (the hardness proof goes through for any $ω=O(n^{1-δ})$, for fixed $0<δ<1$). We describe how DP can be used as a building block in the design of good approximation algorithms. In particular we present a 2-approximation algorithm and a fast polynomial time approximation scheme for the MIS problem in arbitrary $d$-dimensional LoS networks. Finally we comment on how the approach can be adapted to solve a number of important optimization problems in LoS networks.