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cs.DS updates on arXiv.org

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
On the Configuration-LP of the Restricted Assignment Problem
Klaus Jansen, Lars Rohwedder · 2016-11-07 · via cs.DS updates on arXiv.org

We consider the classical problem of Scheduling on Unrelated Machines. In this problem a set of jobs is to be distributed among a set of machines and the maximum load (makespan) is to be minimized. The processing time $p_{ij}$ of a job $j$ depends on the machine $i$ it is assigned to. Lenstra, Shmoys and Tardos gave a polynomial time $2$-approximation for this problem. In this paper we focus on a prominent special case, the Restricted Assignment problem, in which $p_{ij}\in\{p_j,\infty\}$. The configuration-LP is a linear programming relaxation for the Restricted Assignment problem. It was shown by Svensson that the multiplicative gap between integral and fractional solution, the integrality gap, is at most $2 - 1/17 \approx 1.9412$. In this paper we significantly simplify his proof and achieve a bound of $2 - 1/6 \approx 1.8333$. As a direct consequence this provides a polynomial $(2 - 1/6 + ε)$-estimation algorithm for the Restricted Assignment problem by approximating the configuration-LP. The best lower bound known for the integrality gap is $1.5$ and no estimation algorithm with a guarantee better than $1.5$ exists unless $\mathrm{P} = \mathrm{NP}$.