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…
38 Citations
Exploring Parameter Spaces in Coping with Computational Intractability
- Computer Science
- 2014
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”.
A New Algorithm Design Technique for Hard Problems, Building on Methods of Complexity Theory
- Computer ScienceAAIM
- 2018
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.
Exploring Viable Algorithmic Options for Learning from Demonstration (LfD): A Parameterized Complexity Approach
- Computer ScienceArXiv
- 2022
This paper gives the first known restrictions under which efirst known solvability is possible and discusses the implications of thesolvability and unsolvability results for both the basic model of LfD and more complex models of LFD used in practice.
Bypassing Combinatorial Protections: Polynomial-Time Algorithms for Single-Peaked Electorates
- Computer ScienceAAAI
- 2010
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
- Computer Science, MathematicsArXiv
- 2021
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.
Roughly Polynomial Time: A Concept of Tractability Covering All Known Natural NP-complete Problems
- Computer ScienceArXiv
- 2016
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.
On the complexity of detecting convexity over a box
- MathematicsMath. Program.
- 2020
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.
- 2021
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.
Complexity Aspects of Fundamental Questions in Polynomial Optimization
- MathematicsArXiv
- 2020
This thesis settles the computational complexity of some fundamental questions in polynomial optimization, and proposes SDP relaxations for NP-hard problems related to Nash equilibria, such as that of finding the highest achievable welfare under any Nash equilibrium.
References
SHOWING 1-10 OF 68 REFERENCES
A personal view of average-case complexity
- Computer Science, MathematicsProceedings of Structure in Complexity Theory. Tenth Annual IEEE Conference
- 1995
The paper attempts to summarize the state of knowledge in this area, including some "folklore" results that have not explicitly appeared in print, and tries to standardize and unify definitions.
Average-case Complexity
- Mathematics2008 49th Annual IEEE Symposium on Foundations of Computer Science
- 2008
The many open questions and the few things that are known about the average-case complexity of computational problems are reviewed, and a theory of completeness for distributional problems under reductions that preserveaverage-case tractability is initiated.
Hardness Amplification for Errorless Heuristics
- Computer Science48th Annual IEEE Symposium on Foundations of Computer Science (FOCS'07)
- 2007
The question from the standpoint of hardness amplification is studied and it is shown that if every problem in (NP,U) has errorless heuristic circuits that output the correct answer on n -2/9+omicron(1)-fraction of inputs, then (NP.W) has non-uniform errorlessHeuristic schemes.
The Efficiency of Resolution and Davis--Putnam Procedures
- Computer Science, MathematicsSIAM J. Comput.
- 2002
This work gives an algorithm for unsatisfiability that when given an unsatisfiable formula of F finds a resolution proof of F, and investigates a class of backtrack search algorithms for producing resolution refutations of unsatisfiability, commonly known as Davis--Putnam procedures, and gives the first asymptotically tight average-case complexity analysis for their behavior on random formulas.
Pseudorandom Generators, Typically-Correct Derandomization, and Circuit Lower Bounds
- Computer Science, Mathematicscomputational complexity
- 2011
This paper develops a generic approach for constructing typically-correct derandomizations based on seed-extending pseudorandom generators, which are pseudor Frequency generators that reveal their seed.
Truth vs. Proof in Computational Complexity
- PhilosophyBull. EATCS
- 2012
Theoretical Computer Science is blessed (or cursed?) with many open problems. For some of these questions, such as the P vs NP problem, it seems like it could be decades or more before they reach…
The complexity of manipulative attacks in nearly single-peaked electorates
- Political ScienceTARK XIII
- 2011
This paper studies the complexity of manipulative-action algorithms for elections over nearly single-peaked electorates, for various notions of nearness and various election systems.
Junta distributions and the average-case complexity of manipulating elections
- Computer ScienceAAMAS '06
- 2006
It is demonstrated that NP-hard manipulations may be tractable in the average-case, and a family of important voting protocols is susceptible to manipulation by coalitions, when the number of candidates is constant.
Boosting Combinatorial Search Through Randomization
- Computer ScienceAAAI/IAAI
- 1998
This work presents a general method for introducing controlled randomization into complete search algorithms and demonstrates speedups of several orders of magnitude for state-of-the-art complete search procedures running on hard, real-world problems.
Relativized Separations of Worst-Case and Average-Case Complexities for NP
- Mathematics2011 IEEE 26th Annual Conference on Computational Complexity
- 2011
It is shown that the assumption that DistNP is contained in AvgP does not imply that NP =RP byrelativizing techniques, and an oracle is given relative to which the assumption holds but the conclusion fails.