Some easy optimization problems have the overlap-gap property
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866918068601487360 |
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| author | Li, Shuangping Schramm, Tselil |
| author_facet | Li, Shuangping Schramm, Tselil |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01836 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some easy optimization problems have the overlap-gap property Li, Shuangping Schramm, Tselil Computational Complexity Data Structures and Algorithms Combinatorics Probability 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. |
| title | Some easy optimization problems have the overlap-gap property |
| topic | Computational Complexity Data Structures and Algorithms Combinatorics Probability |
| url | https://arxiv.org/abs/2411.01836 |