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

2020
*
arXiv
*
pre-print

This document presents

arXiv:2009.02945v1
fatcat:grzrxnzbmvfphbaicxh47m3wga
*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. ...##
###
A Complexity Dichotomy for Finding Disjoint Solutions of Vertex Deletion Problems
[chapter]

2009
*
Lecture Notes in Computer Science
*

We consider

doi:10.1007/978-3-642-03816-7_28
fatcat:3gifzkyfkbaw3gvaedx5cynmda
*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*. ...##
###
On the Hardness of Finding Optimal Multiple Preset Dictionaries

2004
*
IEEE Transactions on Information Theory
*

We show, however,

doi:10.1109/tit.2004.830778
fatcat:okkaqcc4zbck7cosau2bspqsee
*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. ...##
###
A Complexity Dichotomy for Finding Disjoint Solutions of Vertex Deletion Problems

2011
*
ACM Transactions on Computation Theory
*

We consider

doi:10.1145/1944857.1944860
fatcat:ci3bfpo4r5bulg3g4t4y2n2xly
*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*. ...##
###
Complexity of finite-horizon Markov decision process problems

2000
*
Journal of the ACM
*

Acknowledgements We w ould like to thank Anne Condon, Andy Klapper, Matthew Levy,

doi:10.1145/347476.347480
fatcat:dko66dgsi5cfvph4uzmtkyppqm
*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 . ...##
###
AND-Compression of NP-Complete Problems: Streamlined Proof and Minor Observations

2016
*
Algorithmica
*

The result has implications for the

doi:10.1007/s00453-015-0110-y
fatcat:4szmw2zckbdqrdjozafynjti3i
*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. ...##
###
Infeasibility of instance compression and succinct PCPs for NP

2008
*
Proceedings of the fourtieth annual ACM symposium on Theory of computing - STOC 08
*

[BDFH08]

doi:10.1145/1374376.1374398
dblp:conf/stoc/FortnowS08
fatcat:tur4jkqnr5cjzcwyw3weqr6lbi
*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] . ...##
###
Infeasibility of instance compression and succinct PCPs for NP

2011
*
Journal of computer and system sciences (Print)
*

We show

doi:10.1016/j.jcss.2010.06.007
fatcat:nh4jffjefzemzoizvhmdpxrjse
*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] . ...##
###
AND-compression of NP-complete Problems: Streamlined Proof and Minor Observations
[chapter]

2014
*
Lecture Notes in Computer Science
*

The result has implications for the

doi:10.1007/978-3-319-13524-3_16
fatcat:dimjvdvr6rfhnkmeb7uqymaeqy
*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. ...##
###
Compressed and fully compressed pattern matching in one and two dimensions

2000
*
Proceedings of the IEEE
*

Several related

doi:10.1109/5.892712
fatcat:qvrrcihiq5bljhcegk4oxpspzi
*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*. ...##
###
The Computational Complexity of the Restricted Isometry Property, the Nullspace Property, and Related Concepts in Compressed Sensing
[article]

2013
*
arXiv
*
pre-print

These results are based on the fact

arXiv:1205.2081v6
fatcat:llelyidsand2pk37zwgs3xfscm
*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] . ...##
###
Some Special Cases of a Continuous Time-Cost Tradeoff Problem with Multiple Milestones under a Chain Precedence Graph

2016
*
Management Science and Financial Engineering
*

It has been known

doi:10.7737/msfe.2016.22.1.005
fatcat:wm5zp7zxenbj3l7zyrkq7vu7tq
*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) . ...##
###
Pattern-matching problems for 2-dimensional images described by finite automata
[chapter]

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*. ...

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

2012
*
arXiv
*
pre-print

Finally, we consider formal ways in which theory can help explain the effectiveness

arXiv:1210.8099v1
fatcat:g52yqzbgtjd4bb2jypg6fw6txa
*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. ...##
###
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. ...
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