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A new point of NP-hardness for 2-to-1 Label Cover
[article]

2012
*
arXiv
*
pre-print

We show that given

arXiv:1204.5666v1
fatcat:a5b4kdi6ojc7blmjtrbuqmpdei
*a*satisfiable instance*of*the*2*-*to*-*1**Label**Cover*problem, it is*NP*-*hard**to*find*a*(23/24 + )-satisfying assignment. ...*Of*particular interest is the d =*2*case, i.e.,*2*-*to*-*1**Label**Cover*.*Label**Cover*serves as the starting*point**for*most*NP*-*hardness**of*approximation results. ... Our results In this paper, we focus on proving*NP*-*hardness**for*the*2*-*to*-*1**Label**Cover*problem. ...##
###
A New Point of NP-Hardness for 2-to-1 Label Cover
[chapter]

2012
*
Lecture Notes in Computer Science
*

*For*every integer d ≥

*2*and > 0, there is

*a*

*label*set size q such that it is

*NP*-

*hard*

*to*(

*1*, )-decide the d-

*to*-

*1*

*Label*

*Cover*problem. ... We show that given

*a*satisfiable instance

*of*the

*2*-

*to*-

*1*

*Label*

*Cover*problem, it is

*NP*-

*hard*

*to*find

*a*( 23 24 + )-satisfying assignment. ...

*Of*particular interest is the d =

*2*case, i.e.,

*2*-

*to*-

*1*

*Label*

*Cover*.

*Label*

*Cover*serves as the starting

*point*

*for*most

*NP*-

*hardness*

*of*approximation results. ...

##
###
Near-Optimal Sample Compression for Nearest Neighbors

2018
*
IEEE Transactions on Information Theory
*

23: C(q, i −

doi:10.1109/tit.2018.2822267
fatcat:itmer3jfajfojna2mod246r26q
*1*) ← ∅, N (q, i −*1*) ← {p} Initialize lists*of*p: 24:*NP*-*hard**to*find*a*better compressed set Reduction:• From*Label**Cover*problem,• Reduction holds*for*Euclidean sets too*Label**cover*:• ... Input: Graph, set*of*valid*labels*• Output: Valid*labelling*• Minimization version: Can use multiple colors, minimize number*of**labels*• Dinur and Safra (2004) showed*NP*-*hard**to*approximate within*a*factor ...##
###
Improved Hardness of Approximating Chromatic Number
[article]

2013
*
arXiv
*
pre-print

We prove that

arXiv:1301.5216v3
fatcat:akcrrznhqjhynm3puyq7feoocu
*for*sufficiently large K, it is*NP*-*hard**to*color K-colorable graphs with less than*2*^K^*1*/3 colors. This improves the previous result*of*K versus K^O(log K) in Khot [14]. ... Acknowledgements The author is grateful*to*Siu On Chan*for**pointing*out Theorem E.*1*in his paper, leading*to**a*gap*of*K vs.*2*K*1*/3 , improving the original gap*of*K vs.*2*K*1*/5 . ... Theorem*1*.*For*all sufficiently large K, it is*NP*-*hard**to*color*a*K-colorable graph with*2*K*1*/3 colors. ...##
###
Improved Hardness of Approximating Chromatic Number
[chapter]

2013
*
Lecture Notes in Computer Science
*

We prove that

doi:10.1007/978-3-642-40328-6_17
fatcat:nqgtmn7hrbbfbisaxzzhpsozjy
*for*sufficiently large K, it is*NP*-*hard**to*color K-colorable graphs with less than*2*K*1*/3 colors. This improves the previous result*of*K versus K O(log K) in Khot [14] . ... Acknowledgements The author is grateful*to*Siu On Chan*for**pointing*out Theorem E.*1*in his paper, leading*to**a*gap*of*K vs.*2*K*1*/3 , improving the original gap*of*K vs.*2*K*1*/5 . ... Theorem*1*.*For*all sufficiently large K, it is*NP*-*hard**to*color*a*K-colorable graph with*2*K*1*/3 colors. ...##
###
On NP-Hardness of the Paired de Bruijn Sound Cycle Problem
[chapter]

2013
*
Lecture Notes in Computer Science
*

In this paper we show that the problem

doi:10.1007/978-3-642-40453-5_6
fatcat:lj45sd7qfvflhlgcrvrgozh4yi
*of*checking if there is*a*sound cycle in*a*paired de Bruijn graph is*NP*-*hard*in general case. ... The paired de Bruijn graph is an extension*of*de Bruijn graph incorporating mate pair information*for*genome assembly proposed by Mevdedev et al. ... The problem*of*checking whether*a*paired de Bruijn graph contains*a**covering*sound cycle is*NP*-*hard**for*any fixed |Σ| ≥*2*. ...##
###
On NP-Hardness of the Paired de Bruijn Sound Cycle Problem
[article]

2013
*
arXiv
*
pre-print

In this paper we show that the problem

arXiv:1307.7806v1
fatcat:4tnyye5bvvh6nhzops2egvpqn4
*of*checking if there is*a*sound cycle in*a*paired de Bruijn graph is*NP*-*hard*in general case. ... The paired de Bruijn graph is an extension*of*de Bruijn graph incorporating mate pair information*for*genome assembly proposed by Mevdedev et al. ... The problem*of*checking whether*a*paired de Bruijn graph contains*a**covering*sound cycle is*NP*-*hard**for*any fixed |Σ| ≥*2*. ...##
###
NP-Hardness of Coloring 2-Colorable Hypergraph with Poly-Logarithmically Many Colors

2018
*
International Colloquium on Automata, Languages and Programming
*

We give very short and simple proofs

doi:10.4230/lipics.icalp.2018.15
dblp:conf/icalp/Bhangale18
fatcat:mgbf47aqozgf5dbcg6a33wvnba
*of*the following statements: Given*a**2*-colorable 4-uniform hypergraph on n vertices,*1*. It is*NP*-*hard**to*color it with log δ n colors*for*some δ > 0.*2*. ... It is quasi-*NP*-*hard**to*color it with O log*1*−o(*1*) n colors. ... Can we go beyond poly(log n) coloring*NP*-*hardness*factor*for*coloring*a*c-colorable k-uniform hypergraph*for*some constants c ≥*2*and k ≥ 3? ...##
###
Improved 3LIN Hardness via Linear Label Cover

2019
*
International Workshop on Approximation Algorithms for Combinatorial Optimization
*

The previous best

doi:10.4230/lipics.approx-random.2019.9
dblp:conf/approx/HarshaKLT19
fatcat:vjy5cuwaqbambgcza7ev3gjlu4
*hardness*using*a*polynomial time reduction achieves ε = (log log n) −c , which is obtained by the*Label**Cover**hardness**of*Moshkovitz and Raz [ ... , finds an assignment that satisfies atleast (*1**2*+ ε)-fraction*of*clauses unless*NP*⊆ BPP. ...*For*any constant c > 0,*for*δ =*1*/(log n) c , Gap*Label**Cover*(*1*, δ) is*NP*-*hard*when the*Label**Cover*instance satisfies |Σ*A*|, |Σ B | ≤ |*A*| + |B|. ...##
###
The Projection Games Conjecture and the NP-Hardness of ln n-Approximating Set-Cover

2015
*
Theory of Computing
*

Our work implies that it is

doi:10.4086/toc.2015.v011a007
dblp:journals/toc/Moshkovitz15
fatcat:sg65cikhdre7vdecuqrsmmvjqi
*NP*-*hard**to*approximate SET-*COVER*on instances*of*size N*to*within (*1*− α) ln N*for*arbitrarily small α > 0. ... We establish*a*tight*NP*-*hardness*result*for*approximating the SET-*COVER*problem based on*a*strong PCP theorem. ... Acknowledgments The motivation*to*prove the SET-*COVER*result came from discussions with Ran Raz. ...##
###
On the hardness of approximating label-cover

2004
*
Information Processing Letters
*

The

doi:10.1016/j.ipl.2003.11.007
fatcat:wecu2hhnczbddkgpleetf54rm4
*LABEL*-*COVER*problem, defined by S. Arora, L. Babai, J. Stern ... We prove that*LABEL*-*COVER*is*NP*-*hard**to*approximate*to*within*2*(log n)*1**1*−δ where δ = (log log n) −c*for*any c <*1*/*2*. ... Our reduction will imply that*LABEL*-*COVER*is*NP*-*hard**to*approximate*to*within factor g c (n)*for*any c <*1*/*2*. Our starting*point*is the PCP theorem from [4] . Theorem*1*(PCP Theorem [4] ). ...##
###
Optimal Hub Labeling is NP-complete
[article]

2014
*
arXiv
*
pre-print

We give

arXiv:1407.8373v1
fatcat:7mxmoytfmbce5a4ymb2q75gga4
*a*reduction from the well-known Vertex*Cover*problem on graphs*to*prove that finding an optimal hub*labeling*is indeed*NP*-*hard*. ... The problem*of*assigning as few such hubs as possible was conjectured*to*be*NP*-*hard*, but no proof was known*to*date. ... With Lemma*1*, Lemma*2*and Lemma 3 imply the main theorem which, since Vertex*Cover*is*NP*-*hard*on planar graphs, holds also*for*apex graphs. Theorem*1*. ...##
###
On the Inapproximability of Disjoint Paths and Minimum Steiner Forest with Bandwidth Constraints

2000
*
Journal of computer and system sciences (Print)
*

within ratio

doi:10.1006/jcss.1999.1661
fatcat:ctryptac2vg53akhauyrjqgb24
*2*log*1*&= n unless*NP*DTIME [*2*polylog n ], the integer multicommodity flow problem in directed graphs cannot be approximated within ratio*2*log*1*&= n unless*NP*DTIME[*2*polylog n ], the max ... We show-that the max directed vertex-disjoint paths problem cannot be approximated within ratio*2*log*1*&= n unless*NP*DTIME[*2*polylog n ], the max directed edge-disjoint paths problem cannot be approximated ...*For*any =>0, max*label**cover*cannot be approximated within ratio*2*log*1*&= n unless*NP*DTIME[*2*polylog n ]. The main theorem in this subsection is that DVDP is*hard**to*approximate. ...##
###
New NP-hardness results for 3-Coloring and 2-to-1 Label Cover
[article]

2012
*
arXiv
*
pre-print

In

arXiv:1210.5648v2
fatcat:qjxagczemfdppbflroqazi6geq
*a*related result, we show that given*a*satisfiable instance*of*the*2*-*to*-*1**Label**Cover*problem, it is*NP*-*hard**to*find*a*(23/24 + )-satisfying assignment. ... We show that given*a*3-colorable graph, it is*NP*-*hard**to*find*a*3-coloring with (16/17 + )*of*the edges bichromatic. ...*Of*particular interest is the d =*2*case, i.e.,*2*-*to*-*1**Label**Cover*.*Label**Cover*serves as the starting*point**for*most*NP*-*hardness**of*approximation results. ...##
###
Minimum Constraint Removal Problem for Line Segments is NP-hard
[article]

2021
*
arXiv
*
pre-print

In this paper, using

arXiv:2107.03140v1
fatcat:urgg2siehvadtoolqcmnkuvolm
*a*reduction from Subset Sum problem, in three steps, we show that the problem is*NP*-*hard**for*both weighted and unweighted line segments. ... It has been proved that MCR problem is*NP*-*hard*when constraints have arbitrary shapes or even they are in shape*of*convex polygons. ... Also, one can present approximation or heuristic algorithms*to*solve*new*types*of**NP*-*hard*cases*of*the problem. ...
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