# SIGACT News Complexity Theory Column 76: an atypical survey of typical-case heuristic algorithms

@article{Hemaspaandra2012SIGACTNC, title={SIGACT News Complexity Theory Column 76: an atypical survey of typical-case heuristic algorithms}, author={Lane A. Hemaspaandra and Ryan Williams}, journal={SIGACT News}, year={2012}, volume={43}, pages={70-89} }

Heuristic approaches often do so well that they seem to pretty much always give the right answer. How close can heuristic algorithms get to always giving the right answer, without inducing seismic complexity-theoretic consequences? This article first discusses how a series of results by Berman, Buhrman, Hartmanis, Homer, Longpré, Ogiwara, Schöning, and Watanabe, from the early 1970s through the early 1990s, explicitly or implicitly limited how well heuristic algorithms can do on NP-hard…

## 39 Citations

Exploring Parameter Spaces in Coping with Computational Intractability

- Computer Science
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Three approaches to identify structures which determine the computational complexity of a problem are described, which pave the way for a systematic and clear analysis of computational complexity and they help to chart the “border of intractability”.

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This work focuses on the case when failure means that the algorithm does not return any answer, rather than returning a wrong result, and develops a general algorithm design technique for this type of heuristic algorithms.

The complexity of manipulative attacks in nearly single-peaked electorates

- Political ScienceArtif. Intell.
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Bypassing Combinatorial Protections: Polynomial-Time Algorithms for Single-Peaked Electorates

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This paper shows that for voters who follow the most central political-science model of electorates—single-peaked preferences—those protections vanish, and shows that NP-hard bribery problems—including those for Kemeny and Llull elections—fall to polynomial time.

Logspace Reducibility From Secret Leakage Planted Clique

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The planted clique problem is answered affirmatively for three different statistical problems, namely Sparse PCA, submatrix detection, and testing almost k-wise independence, and there are two ideas involved in implementing known reductions to these problems space efficiently.

Credimus

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This article, written by two complexity theorists who also work in computational social choice theory, focuses on one direction of that process by presenting a brief overview of how most computational complexity theorists view the world.

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- Computer ScienceArXiv
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It appears that every practical decision task (whether in NP or not) can be represented by paddable languages, and, therefore, the RoughP framework applies to all of them.

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The proof shows that the problem of testing whether all matrices in an interval family are positive semidefinite is strongly NP-hard, and in some sense justifies why convexity detection in nonlinear optimization solvers is limited to quadratic functions or functions with special structure.

Existence versus exploitation: the opacity of backdoors and backbones

- Computer ScienceProg. Artif. Intell.
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The theme of this paper is that there is a potential chasm between the existence of such structures in the Boolean formula and being able to effectively exploit them, and one must be very careful not to assume that it is computationally easy to go from theexistence of information tobeing able to get one’s hands on it and/or being ableto exploit it.

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