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Some easy optimization problems have the overlap-gap property

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arxiv 2411.01836 v3 pith:T62FOFT6 submitted 2024-11-04 cs.CC cs.DSmath.COmath.PR

classification cs.CCcs.DSmath.COmath.PR
keywords graphsoverlap-gappathpropertyshortestmathbfoptimizationpolynomial
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abstract

We show that the shortest $s$-$t$ path problem has the overlap-gap property in (i) sparse $\mathbf{G}(n,p)$ graphs and (ii) complete graphs with i.i.d. Exponential edge weights. Furthermore, we demonstrate that in sparse $\mathbf{G}(n,p)$ graphs, shortest path is solved by $O(\log n)$-degree polynomial estimators, and a uniform approximate shortest path can be sampled in polynomial time. This constitutes the first example in which the overlap-gap property is not predictive of algorithmic intractability for a (non-algebraic) average-case optimization problem.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Polynomial-time sampling despite disorder chaos

    cs.CC 2025-08 conditional novelty 8.0 of 10

    Disorder chaos does not prevent polynomial-time Wasserstein sampling: Glauber dynamics samples the hardcore model on G(n,1/2) in O(n) time even though tiny graph perturbations radically change the target distribution.

  2. Computational Complexity of Statistics: New Insights from Low-Degree Polynomials

    math.ST 2025-06 accept novelty 2.0 of 10

    A survey of the low-degree polynomial framework for predicting statistical-computational gaps, covering definitions, evidence, connections to other methods, and open problems.

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