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AND-Compression of NP-Complete Problems: Streamlined Proof and Minor Observations

Holger Dell
2016 Algorithmica  
The result has implications for the compressibility and kernelizability of a whole range of NP-complete parameterized problems. We present a streamlined proof of Drucker's theorem.  ...  Drucker (2012) proved the following result: Unless the unlikely complexity-theoretic collapse coNP is in NP/poly occurs, there is no AND-compression for SAT.  ...  Marx, and anonymous referees for comments on an earlier version of this paper, and Dieter van Melkebeek for some helpful discussions.  ... 
doi:10.1007/s00453-015-0110-y fatcat:4szmw2zckbdqrdjozafynjti3i

AND-compression of NP-complete Problems: Streamlined Proof and Minor Observations [chapter]

Holger Dell
2014 Lecture Notes in Computer Science  
The result has implications for the compressibility and kernelizability of a whole range of NP-complete parameterized problems. We present a streamlined proof of Drucker's theorem.  ...  Drucker (2012) proved the following result: Unless the unlikely complexity-theoretic collapse coNP ⊆ NP/poly occurs, there is no AND-compression for SAT.  ...  Marx, and anonymous referees for comments on an earlier version of this paper, and Dieter van Melkebeek for some helpful discussions.  ... 
doi:10.1007/978-3-319-13524-3_16 fatcat:dimjvdvr6rfhnkmeb7uqymaeqy

FPT Suspects and Tough Customers: Open Problems of Downey and Fellows [chapter]

Fedor V. Fomin, Dániel Marx
2012 Lecture Notes in Computer Science  
We give an update on the status of open problems from the book "Parameterized Complexity" by Downey and Fellows.  ...  Research of the authors was supported by the European Research Council (ERC) grants "Rigorous Theory of Preprocessing," reference 267959, and "PARAMTIGHT: Parameterized complexity and the search for tight  ...  On the other hand, while W[1]-hardness proofs got more streamlined over the years and we have now a better understanding of how to obtain hardness results for certain types of problems (e.g., for planar  ... 
doi:10.1007/978-3-642-30891-8_19 fatcat:2m2ts6wyxjdipafmuov6zxhb4y

Foreword: Special Issue on IPEC 2014

Marek Cygan, Pinar Heggernes
2016 Algorithmica  
Holger Dell in AND-compression of NP-complete problems: Streamlined proof and minor observations presents a streamlined proof of Drucker's theorem.  ...  In Finding Shortest Paths between Graph Colourings, Matthew Johnson, Dieter Kratsch, Stefan Kratsch, Viresh Patel, and Daniël Paulusma give a complete picture of the parameterized complexity of the k-colouring  ... 
doi:10.1007/s00453-016-0151-x fatcat:2xhmdtkgtzbbppmbxnhugehgr4

The Complexity of Translationally Invariant Problems beyond Ground State Energies [article]

James D. Watson, Johannes Bausch, Sevag Gharibian
2020 arXiv   pre-print
-complete, respectively.  ...  Each result also leverages counterintuitive properties of our constructions: for APX-SIM, we "compress" the answers to polynomially many parallel queries to a QMA oracle into a single qubit.  ...  ∀-TI-APX-SIM and TI-APX-SIM are both P QMA EXP -complete for families of Hamiltonians for which the Local Hamiltonian problem is QMA EXP -complete. Proof.  ... 
arXiv:2012.12717v1 fatcat:ya7dzrnsrvfcnpq3eyu2jtncce

New Limits to Classical and Quantum Instance Compression

Andrew Drucker
2012 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science  
Email: andy.drucker@gmail.com. 1 If we could efficiently reduce instances of some NP-complete problem to shorter instances of the same problem, then we could iterate the reduction to solve our problem  ...  We provide such evidence: we show that strong AND-or OR-compression for SAT would imply non-uniform, statistical zero-knowledge proofs for SAT-an even stronger and more unlikely consequence than NP ⊆ coNP  ...  efficient AND-and OR-compression for NP-complete languages.  ... 
doi:10.1109/focs.2012.71 dblp:conf/focs/Drucker12 fatcat:hbk26y3sifhybo7wn2vrb7qlma

New Limits to Classical and Quantum Instance Compression

Andrew Drucker
2015 SIAM journal on computing (Print)  
compression for a large number of natural problems.  ...  Given an instance of a hard decision problem, a limited goal is to compress that instance into a smaller, equivalent instance of a second problem.  ...  efficient AND-and OR-compression for NP-complete languages.  ... 
doi:10.1137/130927115 fatcat:f5lug3s23fdr5k62kfginjm6xm

Complexity analysis and algorithm design for reorganizing data to minimize non-coalesced memory accesses on GPU

Bo Wu, Zhijia Zhao, Eddy Zheng Zhang, Yunlian Jiang, Xipeng Shen
2013 Proceedings of the 18th ACM SIGPLAN symposium on Principles and practice of parallel programming - PPoPP '13  
It systematically analyzes the inherent complexity of the problem in various settings, and for the first time, proves that the problem is NP-complete.  ...  memory accesses for a variety of irregular applications and settings that are beyond the reach of existing techniques.  ...  Acknowledgment We thank Weizhen Mao for her suggestions to one of the NPcompleteness proofs. We owe the anonymous reviewers our gratitude for their helpful comments to the paper.  ... 
doi:10.1145/2442516.2442523 dblp:conf/ppopp/WuZZJS13 fatcat:37gzd4pntfh5rfvdjseygzkbmm

Complexity analysis and algorithm design for reorganizing data to minimize non-coalesced memory accesses on GPU

Bo Wu, Zhijia Zhao, Eddy Zheng Zhang, Yunlian Jiang, Xipeng Shen
2013 SIGPLAN notices  
It systematically analyzes the inherent complexity of the problem in various settings, and for the first time, proves that the problem is NP-complete.  ...  memory accesses for a variety of irregular applications and settings that are beyond the reach of existing techniques.  ...  Acknowledgment We thank Weizhen Mao for her suggestions to one of the NPcompleteness proofs. We owe the anonymous reviewers our gratitude for their helpful comments to the paper.  ... 
doi:10.1145/2517327.2442523 fatcat:5rt2us5q3zcbzcsfhwtpvzrzcy

On Finding and Enumerating Maximal and Maximum k-Partite Cliques in k-Partite Graphs

Charles Phillips, Kai Wang, Erich Baker, Jason Bubier, Elissa Chesler, Michael Langston
2019 Algorithms  
The task of identifying a vertex-maximum element of S is also considered and, in contrast with the k = 2 case, shown to be NP-hard for every k ≥ 3.  ...  A special class of k-partite graphs that arises in the context of functional genomics and other problem domains is studied as well and shown to be more readily solvable via a polynomial-time transformation  ...  Consider the eight-clause Boolean expression It is elementary to verify that each of the eight possible true/false assignments to the elements of {a, b, c} simultaneously one-in-three satisfy exactly three  ... 
doi:10.3390/a12010023 pmid:31448059 pmcid:PMC6707360 fatcat:zdcgd6pe7jdx7pf2knnrzgdngm

Accelerating XOR-based Erasure Coding using Program Optimization Techniques [article]

Yuya Uezato
2021 arXiv   pre-print
We propose a novel approach based on our observation that XOR-based EC virtually generates programs of a Domain Specific Language for XORing byte arrays.  ...  Our optimization flow is three-fold: 1) reducing operations using grammar compression algorithms; 2) reducing memory accesses using deforestation, a functional program optimization method; and 3) reducing  ...  ACKNOWLEDGMENTS We gratefully thank anonymous reviewers for their invaluable and thorough comments, which improved the presentation of this paper and also helped us improve the performance of our experimental  ... 
arXiv:2108.02692v1 fatcat:tyolry4355gt5pqhbferp6pnuu

A Linear Time Parameterized Algorithm for Directed Feedback Vertex Set [article]

Daniel Lokshtanov, M. S. Ramanujan, Saket Saurabh
2016 arXiv   pre-print
On the way to designing our algorithm for DFVS, we give a general methodology to shave off a factor of $n$ from iterative-compression based algorithms for a few other well-studied covering problems in  ...  In the Directed Feedback Vertex Set (DFVS) problem, the input is a directed graph $D$ on $n$ vertices and $m$ edges, and an integer $k$.  ...  The authors thank Dániel Marx for helpful discussions about the polynomial factor of the algorithm for Multicut in [58] .  ... 
arXiv:1609.04347v1 fatcat:fqjriulskjen3fzhaodd3sixa4

Kernelization and Sparseness: the case of Dominating Set [article]

Pål Grønås Drange, Markus S. Dregi, Fedor V. Fomin, Stephan Kreutzer, Daniel Lokshtanov, Marcin Pilipczuk, Michał Pilipczuk, Felix Reidl, Saket Saurabh, Fernando Sánchez Villaamil, Sebastian Siebertz, Somnath Sikdar
2015 arXiv   pre-print
We prove that for every positive integer $r$ and for every graph class $\mathcal G$ of bounded expansion, the $r$-Dominating Set problem admits a linear kernel on graphs from $\mathcal G$.  ...  a linear kernel on $H$-topological-minor-free graphs.  ...  The Graph Motif problem, restricted to graphs G being trees of maximum degree 3, is NP-complete and does not admit a polynomial compression when parameterized by k unless NP ⊆ coNP/poly.  ... 
arXiv:1411.4575v2 fatcat:v7qsnzqyfrfz5bx2pwhfxs6hwq

Low-rank Matrix Completion in a General Non-orthogonal Basis [article]

Abiy Tasissa, Rongjie Lai
2018 arXiv   pre-print
This condition can be computed in time $O(n^3)$ and holds for many cases of deterministic basis where RIP might not hold or is NP hard to verify.  ...  The current approach generalizes the existing analysis for the low-rank matrix completion problem with sampling under entry sensing or with respect to a symmetric orthonormal basis.  ...  For example, for the compressive sensing problem, it has been shown that [2] checking whether RIP holds or not is NP-hard.  ... 
arXiv:1812.05786v1 fatcat:2b7vini7zbcvlljcbfzlg2coae

On the Complexity of Compressing Obfuscation [chapter]

Gilad Asharov, Naomi Ephraim, Ilan Komargodski, Rafael Pass
2018 Lecture Notes in Computer Science  
We view compressing obfuscation as an independent cryptographic primitive and show various positive and negative results concerning its power and plausibility of existence, demonstrating significant differences  ...  In this work, we provide a systematic study of compressing obfuscation, one of the most natural and simple to describe primitives that is known to imply indistinguishability obfuscation when combined with  ...  Acknowledgments We thank Zvika Brakerski for discussions about the possibility of SXiO and XiO with statistical security.  ... 
doi:10.1007/978-3-319-96878-0_26 fatcat:pwdoxk4d2zaubgfd32qfunfbfm
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