A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Satisfiability Allows No Nontrivial Sparsification unless the Polynomial-Time Hierarchy Collapses

2014
*
Journal of the ACM
*

For any integer d ≥ 3 and positive real ǫ we show that if

doi:10.1145/2629620
fatcat:p5rgbdgfujderlax7sxyokquay
*satisfiability*for n-variable d-CNF formulas has a protocol of cost O(n d−ǫ ) then coNP is in NP/poly, which implies that*the**polynomial*-*time**hierarchy*...*The*case d = 2 implies that*no*NP-hard vertex deletion problem based on a graph property that is inherited by subgraphs can have kernels consisting of O(k 2−ǫ ) edges*unless*coNP is in NP/poly, where k ... We would like to thank*the*following people for discussions, comments, pointers to*the*literature, and guidance: Matt Anderson, Albert Atserias, Kord Eickmeyer, Martin ...##
###
Satisfiability allows no nontrivial sparsification unless the polynomial-time hierarchy collapses

2010
*
Proceedings of the 42nd ACM symposium on Theory of computing - STOC '10
*

For any integer d ≥ 3 and positive real ǫ we show that if

doi:10.1145/1806689.1806725
dblp:conf/stoc/DellM10
fatcat:qzmziun5kjdi7dlgmexpan6tne
*satisfiability*for n-variable d-CNF formulas has a protocol of cost O(n d−ǫ ) then coNP is in NP/poly, which implies that*the**polynomial*-*time**hierarchy*...*The*case d = 2 implies that*no*NP-hard vertex deletion problem based on a graph property that is inherited by subgraphs can have kernels consisting of O(k 2−ǫ ) edges*unless*coNP is in NP/poly, where k ... We would like to thank*the*following people for discussions, comments, pointers to*the*literature, and guidance: Matt Anderson, Albert Atserias, Kord Eickmeyer, Martin ...##
###
Best-case and Worst-case Sparsifiability of Boolean CSPs
[article]

2018
*
arXiv
*
pre-print

We continue

arXiv:1809.06171v1
fatcat:al6bgjkptrfp5gjpaerc5crv6i
*the*investigation of*polynomial*-*time**sparsification*for NP-complete Boolean Constraint Satisfaction Problems (CSPs). ...*The*first result essentially shows that for any arity k,*the*only constraint type for which*no**nontrivial**sparsification*is possible has exactly one falsifying assignment, and corresponds to logical OR ...*Satisfiability**allows**no**nontrivial**sparsification**unless**the**polynomial*-*time**hierarchy**collapses*. J. ...##
###
Kernelization Lower Bounds
[chapter]

2013
*
Texts in Computer Science
*

Composition algorithms Simple criterion for ruling out

doi:10.1007/978-1-4471-5559-1_30
fatcat:k35c6pmoaregboa6whaa4pxusq
*polynomial*kernels Simple to understand Not always easy to apply! ... Philip 24/43*Satisfiability**allows**no**nontrivial**sparsification**unless**the**polynomial*-*time**hierarchy**collapses*Dell and van Melkebeek STOC 2010, JACM 2014 Pre-FSTTCS 2014 Workshop Kernelization ... Remark*The*condition coNP ⊆ NP/poly is considered unlikely, because it implies a*collapse*in*the**Polynomial**Hierarchy*. Corollary k-Path does not have a*polynomial*-size kernel,*unless*coNP ⊆ NP/poly. ...##
###
Sparsification Upper and Lower Bounds for Graph Problems and Not-All-Equal SAT

2016
*
Algorithmica
*

of an arbitrary problem, with bitsize O(n 2−ε ) for ε > 0,

doi:10.1007/s00453-016-0189-9
fatcat:6qyiuz6p5vb2jovwn7dbufvzo4
*unless*NP ⊆ coNP/poly and*the**polynomial*-*time**hierarchy**collapses*. ... For*the*problems 4-Coloring, (Directed) Hamiltonian Cycle, and (Connected) Dominating Set, we prove that there is*no**polynomial*-*time*algorithm that reduces any n-vertex input to an equivalent instance, ...*sparsification*of d-nae-sat. ...##
###
Sparsification Upper and Lower Bounds for Graph Problems and Not-All-Equal SAT
[article]

2015
*
arXiv
*
pre-print

of an arbitrary problem, with bitsize O(n^2-e) for e > 0,

arXiv:1509.07437v1
fatcat:mc3xjtofarbd7gcla7vle4cyhe
*unless*NP is in coNP/poly and*the**polynomial*-*time**hierarchy**collapses*. ... For*the*problems 4-Coloring, (Directed) Hamiltonian Cycle, and (Connected) Dominating Set, we prove that there is*no**polynomial*-*time*algorithm that reduces any n-vertex input to an equivalent instance, ... v) ⊆ [4] of*allowed*colors. ...##
###
On Sparsification for Computing Treewidth
[article]

2013
*
arXiv
*
pre-print

of an arbitrary problem, with O(n^2-e) bits, then NP is in coNP/poly and

arXiv:1308.3665v1
fatcat:ensn3iaj75dqff2mfiabif6due
*the**polynomial**hierarchy**collapses*to its third level. ... for any e > 0,*unless*NP is in coNP/poly. ... equivalent instances of an arbitrary problem, with O(n 2− ) bits, for some > 0, then NP ⊆ coNP/poly and*the**polynomial**hierarchy**collapses*[27] . ...##
###
Co-nondeterminism in compositions: A kernelization lower bound for a Ramsey-type problem
[article]

2011
*
arXiv
*
pre-print

(JCSS 2009) showed that,

arXiv:1107.3704v2
fatcat:qns7jo4gfjdwrekuylmhc7iwju
*unless*NP \subseteq coNP/poly,*the*existence of a deterministic*polynomial*-*time*composition algorithm, i.e., an algorithm which outputs an instance of bounded parameter value which ... Thus we show that,*unless*NP \subseteq coNP/poly,*the*problem does not admit a kernelization with*polynomial*size guarantee. ... Acknowledgement*The*author is grateful to Pascal Schweitzer for providing Lemma 5 and for many useful comments on*the*paper. ...##
###
The Landscape of Communication Complexity Classes

2018
*
Computational Complexity
*

*the*full version), and

*no*

*nontrivial*lower bounds against it are known for any explicit function. ... One of

*the*most notorious open problems in communication complexity is to prove lower bounds against

*the*analogue of

*the*

*polynomial*

*hierarchy*(PH) for any explicit two-party function. ... However, it is unlikely that US ⊆ coDP: [10] showed that this inclusion cannot hold in

*the*classical

*time*-bounded setting

*unless*

*the*

*polynomial*

*hierarchy*

*collapses*. ...

##
###
Introducing lop-kernels: a framework for kernelization lower bounds
[article]

2021
*
arXiv
*
pre-print

Finally, we prove that MMVC does not admit

arXiv:2102.02484v3
fatcat:fzq4726v7feydmutjof6zvkik4
*polynomial*kernels parameterized by*the*size of a minimum vertex cover of*the*input graph, even on bipartite graphs,*unless*NP⊆ coNP / poly. ... ,*the*paw, or*the*complete graphs, by making use of*the*Erdös-Hajnal property. ...*Satisfiability**allows**no**nontrivial**sparsification**unless**the**polynomial*-*time**hierarchy**collapses*. Journal of*the*ACM, 61(4):23:1–23:27, 2014. doi:10.1145/2629620. 29 Reinhard Diestel. ...##
###
Network Sparsification for Steiner Problems on Planar and Bounded-Genus Graphs
[article]

2017
*
arXiv
*
pre-print

In

arXiv:1306.6593v4
fatcat:oddhcwecevg5xhyo5mlqkzl3gm
*the*language of parameterized complexity, these results imply*the*first*polynomial*kernels for Steiner Tree and Steiner Forest on planar and bounded-genus graphs (parameterized by*the*size of*the*tree ... and a terminal set S ⊆ V(G), one can in*polynomial**time*find a set F ⊆ E(G) that contains an optimal (edge) multiway cut C separating S and that has size*polynomial*in |C|. ... [5] can be strengthened to also refute a subexponential-*time*algorithm. ...##
###
Sparsification Upper and Lower Bounds for Graphs Problems and Not-All-Equal SAT *

unpublished

of an arbitrary problem, with bitsize O(n 2−ε) for ε > 0,

fatcat:352dbfeblvdtddiii7iizqkvoe
*unless*NP ⊆ coNP/poly and*the**polynomial*-*time**hierarchy**collapses*. ... For*the*problems 4-Coloring, (Directed) Hamiltonian Cycle, and (Connected) Dominating Set, we prove that there is*no**polynomial*-*time*algorithm that reduces any n-vertex input to an equivalent instance, ... be encoded in O(n 2−ε ) bits, then NP ⊆ coNP/poly and*the**polynomial*-*time**hierarchy**collapses*. ...##
###
Nondeterministic Direct Product Reductions and the Success Probability of SAT Solvers

2013
*
2013 IEEE 54th Annual Symposium on Foundations of Computer Science
*

In these theorems one assumes that a target function f is mildly hard against nondeterministic circuits, and concludes that

doi:10.1109/focs.2013.84
dblp:conf/focs/Drucker13
fatcat:vcqxpllt3vedbacdlbsc5mwjdi
*the*direct product f ⊗t is extremely hard against (only*polynomially*smaller) ... As an application, we show that if NP is not in coNP/poly then, for every PPT algorithm attempting to produce*satisfying*assigments to Boolean formulas, there are infinitely many instances where*the*algorithm's ...*The*hypothesis that*the**Polynomial**Hierarchy*does not*collapse*to Σ p 3 can be equivalently restated as one such assumption: namely, that there is*no**polynomial*-*time*procedure that reduces a 4-round game ...##
###
Network Sparsification for Steiner Problems on Planar and Bounded-Genus Graphs

2014
*
2014 IEEE 55th Annual Symposium on Foundations of Computer Science
*

van (2014) Network

doi:10.1109/focs.2014.37
dblp:conf/focs/PilipczukPSL14
fatcat:33nagim3pvejpkiakhdive3zsy
*sparsification*for Steiner problems on planar and bounded-genus graphs. ... [5] can be strengthened to also refute a subexponential-*time*algorithm. ... Acknowledgements We thank Daniel Lokshtanov and Saket Saurabh for showing us*the*application of Baker's approach to Planar Multiway Cut (Theorem 13.1) and for*allowing*us to include*the*proof in this paper ...##
###
The Complexity of Propositional Proofs

2007
*
Bulletin of Symbolic Logic
*

Questions about proof sizes have connections with computational complexity, theories of arithmetic, and

doi:10.2178/bsl/1203350879
fatcat:mzffx4yqzfcg7ell47v452f2eu
*satisfiability*algorithms. ... AbstractPropositional proof complexity is*the*study of*the*sizes of propositional proofs, and more generally,*the*resources necessary to certify propositional tautologies. ...*The*author wishes to thank Paul Beame for answering some questions on [33] and [2] , and also for providing Figure 8 . ...
« Previous

*Showing results 1 — 15 out of 23 results*