Filters








11,032 Hits in 6.4 sec

A Simpler NP-Hardness Proof for Familial Graph Compression [article]

Ammar Ahmed, Zohair Raza Hassan, Mudassir Shabbir
2020 arXiv   pre-print
This document presents a simpler proof showcasing the NP-hardness of Familial Graph Compression.  ...  FGC is NP-complete when G is a connected, simple graph, H is the single node graph, and F is a family of graphlets or motifs.  ...  This problem was proven to be NP-complete in [3] . Note that for our reduction, the fact that "each element appears in no more than three subsets" is inconsequential. Theorem 3.1. XC3 ≤ P FGC.  ... 
arXiv:2009.02945v1 fatcat:grzrxnzbmvfphbaicxh47m3wga

A Complexity Dichotomy for Finding Disjoint Solutions of Vertex Deletion Problems [chapter]

Michael R. Fellows, Jiong Guo, Hannes Moser, Rolf Niedermeier
2009 Lecture Notes in Computer Science  
We consider a large class of vertex deletion problems on undirected graphs and show that, except for few cases which are polynomial-time solvable, the others are NP-complete.  ...  We investigate the computational complexity of a general "compression task" centrally occurring in the recently developed technique of iterative compression for exactly solving NP-hard minimization problems  ...  NP-Hardness Framework and Simple Proofs Lewis and Yannakakis [12] showed that Π-Vertex Deletion for any non-trivial hereditary property Π is NP-complete.  ... 
doi:10.1007/978-3-642-03816-7_28 fatcat:3gifzkyfkbaw3gvaedx5cynmda

On the Hardness of Finding Optimal Multiple Preset Dictionaries

M. Mitzenmacher
2004 IEEE Transactions on Information Theory  
We show, however, that nding optimal multiple preset dictionaries for Hu man and LZ77based compression schemes is NP-hard.  ...  Preset dictionaries for Hu man codes are used e ectively in fax transmission and JPEG encoding. A natural extension is to allow multiple preset dictionaries instead of just one.  ...  We have instead shown that the problem is NP-hard by showing a reduction to a simple and useful NP-hard problem, catalog segmentation. In practice, approximations would clearly be suitable.  ... 
doi:10.1109/tit.2004.830778 fatcat:okkaqcc4zbck7cosau2bspqsee

A Complexity Dichotomy for Finding Disjoint Solutions of Vertex Deletion Problems

Michael R. Fellows, Jiong Guo, Hannes Moser, Rolf Niedermeier
2011 ACM Transactions on Computation Theory  
We consider a large class of vertex deletion problems on undirected graphs and show that, except for few cases which are polynomial-time solvable, the others are NP-complete.  ...  We investigate the computational complexity of a general "compression task" centrally occurring in the recently developed technique of iterative compression for exactly solving NP-hard minimization problems  ...  NP-Hardness Framework and Simple Proofs Lewis and Yannakakis [12] showed that Π-Vertex Deletion for any non-trivial hereditary property Π is NP-complete.  ... 
doi:10.1145/1944857.1944860 fatcat:ci3bfpo4r5bulg3g4t4y2n2xly

Complexity of finite-horizon Markov decision process problems

Martin Mundhenk, Judy Goldsmith, Christopher Lusena, Eric Allender
2000 Journal of the ACM  
Acknowledgements We w ould like to thank Anne Condon, Andy Klapper, Matthew Levy, and especially Michael Littman for discussions and suggestions on this material.  ...  Proof. It is clear that the problem is in NP. In order to show its completeness, we give a reduction from the NP-complete problem PARTITION. The instances of PARTITION are functions f : n !  ...  One major contribution of this paper is a natural problem that is complete for the class NP PP .  ... 
doi:10.1145/347476.347480 fatcat:dko66dgsi5cfvph4uzmtkyppqm

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.  ...  An AND-compression is a deterministic polynomial-time algorithm that maps a set of SAT-instances x_1,...  ...  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

Infeasibility of instance compression and succinct PCPs for NP

Lance Fortnow, Rahul Santhanam
2008 Proceedings of the fourtieth annual ACM symposium on Theory of computing - STOC 08  
[BDFH08] and Harnik and Naor [HN06b] and has a number of implications. • A number of parametric NP problems, including Satisfiability, Clique, Dominating Set and Integer Programming, are not instance compressible  ...  We show that there is no reduction from OR-SAT to any set A where the length of the output is bounded by a polynomial in n, unless NP ⊆ coNP/poly, and the Polynomial-Time Hierarchy collapses.  ...  Acknowledgements We thank Hans Bodlaender, Rod Downey, Mike Fellows and Danny Hermelin for bringing Question 1.1 to our attention and sending us an early version of their manuscript [BDFH08] .  ... 
doi:10.1145/1374376.1374398 dblp:conf/stoc/FortnowS08 fatcat:tur4jkqnr5cjzcwyw3weqr6lbi

Infeasibility of instance compression and succinct PCPs for NP

Lance Fortnow, Rahul Santhanam
2011 Journal of computer and system sciences (Print)  
We show that there is no reduction from OR-SAT to any set A where the length of the output is bounded by a polynomial in n, unless NP ⊆ coNP/poly, and the Polynomial-Time Hierarchy collapses.  ...  (i) A number of parametric NP problems, including Satisfiability, Clique, Dominating Set and Integer Programming, are not instance compressible or polynomially kernelizable unless NP ⊆ coNP/poly.  ...  Acknowledgments We thank Hans Bodlaender, Rod Downey, Mike Fellows and Danny Hermelin for bringing Question 1.1 to our attention and sending us an early version of their manuscript [6] .  ... 
doi:10.1016/j.jcss.2010.06.007 fatcat:nh4jffjefzemzoizvhmdpxrjse

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.  ...  An AND-compression is a deterministic polynomial-time algorithm that maps a set of SAT-instances x 1 , . . . , x t to a single SAT-instance y of size poly(max i |x i |) such that y is satisfiable if and  ...  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

Compressed and fully compressed pattern matching in one and two dimensions

W. Rytter
2000 Proceedings of the IEEE  
Several related problems for compressed strings and arrays are considered: equality testing, computation of regularities, subsegment extraction, language membership, and solvability of word equations.  ...  We survey the complexity issues related to several algorithmic problems for compressed and fully compressed pattern matching in one-and two-dimensional texts without explicit decompression.  ...  Proof: The proof of NP-hardness is a reduction from the SUBSET SUM problem. We can construct easily a straight-line program such that and .  ... 
doi:10.1109/5.892712 fatcat:qvrrcihiq5bljhcegk4oxpspzi

The Computational Complexity of the Restricted Isometry Property, the Nullspace Property, and Related Concepts in Compressed Sensing [article]

Andreas M. Tillmann, Marc E. Pfetsch
2013 arXiv   pre-print
These results are based on the fact that determining the spark of a matrix is NP-hard, which is also established in this paper.  ...  We confirm these conjectures by showing that for a given matrix A and positive integer k, computing the best constants for which the RIP or NSP hold is, in general, NP-hard.  ...  Since by definition the complementary problem of an NP-complete problem is coNP-complete, the respective hardness results follow-see also [4] .  ... 
arXiv:1205.2081v6 fatcat:llelyidsand2pk37zwgs3xfscm

Some Special Cases of a Continuous Time-Cost Tradeoff Problem with Multiple Milestones under a Chain Precedence Graph

Byung-Cheon Choi, Jibok Chung
2016 Management Science and Financial Engineering  
It has been known that the problems with the concave and the convex cost functions for the compression are NP-hard and polynomially solvable, respectively.  ...  We consider a time-cost tradeoff problem with multiple milestones under a chain precedence graph. In the problem, some penalty occurs unless a milestone is completed before its appointed date.  ...  Theorem 3: The decision version of the concave-TCTP-f is NP-complete. Proof: The proof is by reduction from the partition problem which is known to be NP-complete (Garey and Johnson, 1979) .  ... 
doi:10.7737/msfe.2016.22.1.005 fatcat:wm5zp7zxenbj3l7zyrkq7vu7tq

Pattern-matching problems for 2-dimensional images described by finite automata [chapter]

Juhani Karhumäki, Wojciech Plandowski, Wojciech Rytter
1997 Lecture Notes in Computer Science  
Compressed matching for weighted automata is NP-complete. Fully compressed pattern-checking for deterministic automata is in P. Fully compressed matching for deterministic automata is NP-complete.  ...  is given explicitely and the text is compressed.  ...  This completes the proof. 2 Theorem 3.3 Compressed matching for weighted automata is NP-complete. Proof: First we show that the problem is in NP.  ... 
doi:10.1007/bfb0036188 fatcat:geznmgm7tzgcxox724y2xjbn6y

An Atypical Survey of Typical-Case Heuristic Algorithms [article]

Lane A. Hemaspaandra, Ryan Williams
2012 arXiv   pre-print
Finally, we consider formal ways in which theory can help explain the effectiveness of heuristics that solve NP-hard problems in practice.  ...  limited how well heuristic algorithms can do on NP-hard problems.  ...  And in the previous section, we mentioned that by padding it is simple to make even NP-complete problems that are easy on all but 2 n ε of their inputs.  ... 
arXiv:1210.8099v1 fatcat:g52yqzbgtjd4bb2jypg6fw6txa

Page 5689 of Mathematical Reviews Vol. , Issue 99h [page]

1999 Mathematical Reviews  
to efficiently solve a problem known to be NP-hard.  ...  A PCP is a proof for an NP-statement that can be checked extremely efficiently by a probabilistic verifier.  ... 
« Previous Showing results 1 — 15 out of 11,032 results