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Parameterized Intractability of Even Set and Shortest Vector Problem
[article]

2019
*
arXiv
*
pre-print

We also consider the

arXiv:1909.01986v1
fatcat:qiymsq5hkrdffimvj2d4dfl4pi
*parameterized*k-*Shortest**Vector**Problem*(SVP), in which we are given a lattice whose basis*vectors*are integral*and*an integer k,*and*the goal is to determine whether the norm*of*the ... The k-*Even**Set**problem*is a*parameterized*variant*of*the Minimum Distance*Problem**of*linear codes over F_2, which can be stated as follows: given a generator matrix A*and*an integer k, determine whether ... Pasin would like to thank Danupon Nanongkai for introducing him to the k-*Even**Set**problem**and*for subsequent useful discussions. ...##
###
Parameterized Intractability of Even Set and Shortest Vector Problem from Gap-ETH
[article]

2018
*
arXiv
*
pre-print

We also consider the

arXiv:1803.09717v1
fatcat:ymowevvnkvg3dktbbzbpf3cezi
*parameterized*k-*Shortest**Vector**Problem*(SVP), in which we are given a lattice whose basis*vectors*are integral*and*an integer k,*and*the goal is to determine whether the norm*of*the ... The k-*Even**Set**problem*is a*parameterized*variant*of*the Minimum Distance*Problem**of*linear codes over F_2, which can be stated as follows: given a generator matrix A*and*an integer k, determine whether ... Pasin would like to thank Danupon Nanongkai for introducing him to the k-*Even**Set**problem**and*for subsequent useful discussions. ...##
###
Parameterized Intractability of Even Set and Shortest Vector Problem from Gap-ETH

2018
*
International Colloquium on Automata, Languages and Programming
*

We also consider the

doi:10.4230/lipics.icalp.2018.17
dblp:conf/icalp/BhattacharyyaGS18
fatcat:hrycg3ktk5code4aclejrfkozi
*parameterized*k-*Shortest**Vector**Problem*(SVP), in which we are given a lattice whose basis*vectors*are integral*and*an integer k,*and*the goal is to determine whether the norm*of*the ... The k-*Even**Set**problem*is a*parameterized*variant*of*the Minimum Distance*Problem**of*linear codes over F 2 , which can be stated as follows: given a generator matrix A*and*an integer k, determine whether ... (Equivalently, this means that the message length must be at least h − (d/2 + O(1)) log h.) 0 1 8 17:6*Parameterized**Intractability**of**Even**Set**and**Shortest**Vector**Problem*dense Dumer et al.introduce ...##
###
Resolving Infeasibility of Linear Systems: A Parameterized Approach

2019
*
International Symposium on Parameterized and Exact Computation
*

On the one hand, we establish

doi:10.4230/lipics.ipec.2019.17
dblp:conf/iwpec/GokeCM19
fatcat:sgby4wvmi5ep7duyx3d5noigo4
*parameterized**intractability*(W[1]-hardness) results*even*in very restricted*settings*. ... Our algorithms capture the case*of*Directed Feedback Arc*Set*, a fundamental*parameterized**problem*whose fixed-parameter tractability was shown by Chen et al. ... Acknowledgements We thank an anonymous reviewer*of*an earlier version for a suggestion on run time improvements. ...##
###
Revenue maximization in Stackelberg Pricing Games: beyond the combinatorial setting

2020
*
Mathematical programming
*

Second, we study the

doi:10.1007/s10107-020-01495-0
fatcat:ecwzi4jwcvez5a4pl6gpaoncti
*parameterized*complexity*of*computing the optimal revenue with respect to the number k*of*priceable items. ... In a Stackelberg Pricing Game a distinguished player, the leader, chooses prices for a*set**of*items,*and*the other players, the followers, each seeks to buy a minimum cost feasible subset*of*the items. ... This holds true*even*in a very restricted combinatorial*setting*. The second part*of*the paper deals with the*parameterized*complexity*of*Stackelberg Pricing Games (Section 3). ...##
###
A Parameterized Complexity Analysis of Combinatorial Feature Selection Problems
[chapter]

2013
*
Lecture Notes in Computer Science
*

We provide tractability as well as

doi:10.1007/978-3-642-40313-2_40
fatcat:puma4phsvbavlfgtrelxhianoy
*intractability*results; for example, we show that the Distinct*Vectors**problem*on binary points is polynomial-time solvable if each pair*of*points differs in at most ... In*parameterized*complexity analysis, one seeks to identify relevant*problem*-specific quantities*and*tries to determine their influence on the computational complexity*of*the considered*problem*. ... We are grateful to anonymous MFCS referees for extensive*and*constructive feedback. ...##
###
Cryptography without (Hardly Any) Secrets ?
[chapter]

2009
*
Lecture Notes in Computer Science
*

In recent years, starting with the work on physically observable cryptography by [MR04] Micali

doi:10.1007/978-3-642-01001-9_21
fatcat:sh4xu66h5fbbhjckvyluw2d6oa
*and*Reyzin, a new goal has been*set*to build a general theory*of*physical security against a large class*of*... data*and*secret keys. ... Its security is based on the computationally*intractability**of*the learning with errors (LWE)*problem*which is related to the*intractability**of*approximating the length*of*the*shortest**vector*in an integer ...##
###
Designing Lookahead Policies for Sequential Decision Problems in Transportation and Logistics

2022
*
IEEE Open Journal of Intelligent Transportation Systems
*

There is a wide range

doi:10.1109/ojits.2022.3148574
fatcat:qs6zp4yobvh33knl3ibo573e44
*of*sequential decision*problems*in transportation*and*logistics that require dealing with uncertainty. ... There are four classes*of*policies that we can draw on for different types*of*decisions, but many*problems*in transportation*and*logistics will ultimately require some form*of*direct lookahead policy ( ...*Shortest*path*problems*are easy to solve using dynamic programming, but if we have a dynamic*shortest*path*problem*with link costs changing over time, the entire*vector**of*link costs needs to be included ...##
###
Complexity of Reconfiguration Problems for Constraint Satisfaction
[article]

2018
*
arXiv
*
pre-print

In this paper, we study the

arXiv:1812.10629v1
fatcat:eeczguy7fzgthjwtmeybl2pjqm
*problem*from the viewpoints*of*polynomial-time solvability*and**parameterized*complexity,*and*give several interesting boundaries*of*tractable*and**intractable*cases. ... Constraint satisfaction*problem*(CSP) is a well-studied combinatorial search*problem*, in which we are asked to find an assignment*of*values to given variables so as to satisfy all*of*given constraints. ... Acknowledgements This work is partially supported by JST CREST Grant Number JPMJCR1402,*and*by JSPS KAKENHI Grant Numbers JP18H04091, JP16J02175, JP16K00003,*and*JP16K00004, Japan. ...##
###
On the parameterized complexity of Compact Set Packing
[article]

2022
*
arXiv
*
pre-print

The

arXiv:2111.06338v3
fatcat:hpfgrtujtfcclfycz5g3ruvyiy
*Set*Packing*problem*is, given a collection*of**sets*𝒮 over a ground*set*𝒰, to find a maximum collection*of**sets*that are pairwise disjoint. ... The focus*of*this work is on*parameterized*complexity,*Parameterized**Set*Packing (PSP): Given r ∈ℕ, is there a collection 𝒮' ⊆𝒮: |𝒮'| = r such that the*sets*in 𝒮' are pairwise disjoint? ... Acknowledgment: I thank Parinya Chalermsook for the informative discussions about the results*of*the paper,*and*for providing guidance on writing this paper. ...##
###
A Survey on Approximation in Parameterized Complexity: Hardness and Algorithms
[article]

2020
*
arXiv
*
pre-print

*Parameterization*

*and*approximation are two popular ways

*of*coping with NP-hard

*problems*. More recently, the two have also been combined to derive many interesting results. ... We survey developments in the area both from the algorithmic

*and*hardness perspectives, with emphasis on new techniques

*and*potential future research directions. ... Conflicts

*of*Interest: The authors declare no conflict

*of*interest. ...

##
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A Survey on Approximation in Parameterized Complexity: Hardness and Algorithms

2020
*
Algorithms
*

*Parameterization*

*and*approximation are two popular ways

*of*coping with NP-hard

*problems*. More recently, the two have also been combined to derive many interesting results. ... We survey developments in the area both from the algorithmic

*and*hardness perspectives, with emphasis on new techniques

*and*potential future research directions. ... Conflicts

*of*Interest: The authors declare no conflict

*of*interest. ...

##
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Separating sets of strings by finding matching patterns is almost always hard

2017
*
Theoretical Computer Science
*

We then perform a detailed

doi:10.1016/j.tcs.2016.12.018
fatcat:jciozho3inbkfdqqmaynqedhum
*parameterized*analysis*of*the*problem*, separating tractable*and**intractable*variants. ... In particular we show that*parameterizing*by the size*of*pattern*set**and*the number*of*strings,*and*the size*of*the alphabet*and*the number*of*strings give FPT results, amongst others. ...*Even*if we take the length*of*the strings as the parameter, the*problem*is para-NP-complete. Table 1 gives a summary*of*the*parameterized*results,*and*some key open*problems*. ...##
###
Consistent mesh parameterizations

2001
*
Proceedings of the 28th annual conference on Computer graphics and interactive techniques - SIGGRAPH '01
*

In this paper we propose an algorithm which establishes

doi:10.1145/383259.383277
dblp:conf/siggraph/PraunSS01
fatcat:lvnt3lyp6vge3g32qd3wekds6i
*parameterizations*for a*set**of*models. ... Figure 1 : When given a*set**of*head models an obvious shape to compute is their average. ... Models are courtesy Cyberware, Stanford University, Max Planck Institut für Computer Graphik,*and*the University*of*Washington. ...##
###
Longest common subsequence problem for unoriented and cyclic strings

2007
*
Theoretical Computer Science
*

We show that these

doi:10.1016/j.tcs.2006.10.002
fatcat:qeb4m4ritfhwpckte46dqx2kby
*problems*are NP-hard,*and*W[1]-hard if*parameterized*in the number*of*input strings. ... Moreover, we study the approximability*of*these*problems*: we discuss the existence*of*approximation bounds depending on the cardinality*of*the alphabet, on the length*of*the*shortest*sequence,*and*on the ... However, when the number*of*input strings is unbounded, LCS becomes*intractable*. •*Even*for binary alphabets, the decision*problem*associated with LCS is NP-hard [16] ,*and*W[1]-hard when*parameterized*...
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