Approximating Solution Structure

Approximations can aim at having close to optimal value or, alternatively, they can aim at structurally resembling an optimal solu- tion. Whereas value-approximation has been extensively studied by com- plexity theorists over the last three decades, structural-approximation has not yet been defined, let alone studied. However, structural- approximation is theoretically no less interesting, and has important ap- plications in cognitive science. Building on analogies with existing value- approximation algorithms and classes, we develop a general framework for analyzing structural (in)approximability. We identify dissociations between solution value and solution structure, and generate a list of open problems that may stimulate future research.

[1]  J. Tenenbaum,et al.  Intuitive theories as grammars for causal inference , 2007 .

[2]  Vijay V. Vazirani,et al.  Approximation Algorithms , 2001, Springer Berlin Heidelberg.

[3]  E. Millgram.  Coherence: The Price of the Ticket , 2000 .

[4]  J. Tenenbaum,et al.  Probabilistic models of cognition. Special Issue. , 2006 .

[5]  김동규,et al.  [서평]「Algorithms on Strings, Trees, and Sequences」 , 2000 .

[6]  Paul Thagard,et al.  Coherence as Constraint Satisfaction , 2019, Cogn. Sci..

[7]  Marcello Frixione,et al.  Tractable Competence , 2001, Minds and Machines.

[8]  Zhi-Zhong Chen,et al.  On the Complexity of Computing Optimal Solutions , 1990, Int. J. Found. Comput. Sci..

[9]  J. Tenenbaum,et al.  Special issue on “Probabilistic models of cognition , 2022 .

[10]  Nick Chater,et al.  A simplicity principle in unsupervised human categorization , 2002, Cogn. Sci..

[11]  Giorgio Gambosi,et al.  Complexity and approximation: combinatorial optimization problems and their approximability properties , 1999 .

[12]  Uriel Feige,et al.  Approximating the value of two power proof systems, with applications to MAX 2SAT and MAX DICUT , 1995, Proceedings Third Israel Symposium on the Theory of Computing and Systems.

[13]  I. Rooij.  Tractable cognition : complexity theory in cognitive psychology , 2003 .

[14]  Dana Ron,et al.  Distance Approximation in Bounded-Degree and General Sparse Graphs , 2006, APPROX-RANDOM.

[15]  Michael R. Fellows,et al.  Parameterized complexity analysis in computational biology , 1995, Comput. Appl. Biosci..

[16]  李幼升,et al.  Ph , 1989 .

[17]  J. Håstad.  Clique is hard to approximate withinn1−ε , 1999 .

[18]  Klaus Jansen,et al.  Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques , 2012, Lecture Notes in Computer Science.

[19]  Mihalis Yannakakis,et al.  Optimization, approximation, and complexity classes , 1991, STOC '88.

[20]  Oded Goldreich,et al.  Combinatorial property testing (a survey) , 1997, Randomization Methods in Algorithm Design.

[21]  Michael R. Fellows,et al.  The Parameterized Complexity of Sequence Alignment and Consensus , 1994, CPM.

[22]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[23]  Dániel Marx,et al.  Parameterized Complexity and Approximation Algorithms , 2008, Comput. J..

[24]  Jonas Holmerin,et al.  Clique Is Hard to Approximate within n1-o(1) , 2000, ICALP.