Dagstuhl Seminar Proceedings, Volume 9511
Dagstuhl Seminar Proceedings
DagSemProc
https://www.dagstuhl.de/dagpub/1862-4405
https://dblp.org/db/series/dagstuhl
1862-4405
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
9511
2010
https://drops.dagstuhl.de/entities/volume/DagSemProc-volume-9511
09511 Abstracts Collection – Parameterized complexity and approximation algorithms
From 14. 12. 2009 to 17. 12. 2009., the Dagstuhl Seminar 09511
``Parameterized complexity and approximation algorithms '' was held
in Schloss Dagstuhl~--~Leibniz Center for Informatics.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available.
Parameterized complexity
Approximation algorithms
1-14
Regular Paper
Erik D.
Demaine
Erik D. Demaine
MohammadTaghi
Hajiaghayi
MohammadTaghi Hajiaghayi
Dániel
Marx
Dániel Marx
10.4230/DagSemProc.09511.1
Creative Commons Attribution 4.0 International license
https://creativecommons.org/licenses/by/4.0/legalcode
09511 Executive Summary – Parameterized complexity and approximation algorithms
Many of the computational problems that arise in practice are optimization
problems: the task is to find a solution where the cost, quality, size,
profit, or some other measure is as large or small as possible. The
NP-hardness of an optimization problem implies that, unless P = NP, there is
no polynomial-time algorithm that finds the exact value of the optimum.
Various approaches have been proposed in the literature to cope with NP-hard
problems. When designing approximation algorithms, we relax the requirement
that the algorithm produces an optimum solution, and our aim is to devise a
polynomial-time algorithm such that the solution it produces is not
necessarily optimal, but there is some worst-case bound on the solution
quality.
Parameterized complexity
Approximation algorithms
1-0
Regular Paper
Erik D.
Demaine
Erik D. Demaine
MohammadTaghi
Hajiaghayi
MohammadTaghi Hajiaghayi
Dániel
Marx
Dániel Marx
10.4230/DagSemProc.09511.2
Creative Commons Attribution 4.0 International license
https://creativecommons.org/licenses/by/4.0/legalcode
09511 Open Problems – Parameterized complexity and approximation algorithms
The paper contains a list of the problems presented on Monday, December 14, 2009 at the open problem session of the Seminar on Parameterized Complexity and Approximation Algorithms, held at Schloss Dagstuhl in Wadern, Germany.
Parameterized complexity
approximation algorithms
open problems
1-10
Regular Paper
Erik D.
Demaine
Erik D. Demaine
MohammadTaghi
Hajiaghayi
MohammadTaghi Hajiaghayi
Dániel
Marx
Dániel Marx
10.4230/DagSemProc.09511.3
Creative Commons Attribution 4.0 International license
https://creativecommons.org/licenses/by/4.0/legalcode
Approximating minimum cost connectivity problems
We survey approximation algorithms of connectivity problems.
The survey presented describing various techniques. In the talk the following techniques and results are presented.
1)Outconnectivity: Its well known that there exists a polynomial time algorithm to solve the problems of finding an edge k-outconnected from r subgraph [EDMONDS] and a vertex k-outconnectivity subgraph from r [Frank-Tardos] .
We show how to use this to obtain a ratio 2 approximation for the min cost edge k-connectivity
problem.
2)The critical cycle theorem of Mader: We state a fundamental theorem of Mader and use it to provide a 1+(k-1)/n ratio approximation for the min cost vertex k-connected subgraph, in the metric case.
We also show results for the min power vertex k-connected problem using this lemma.
We show that the min power is equivalent to the min-cost case with respect to approximation.
3)Laminarity and uncrossing: We use the well known laminarity of a BFS solution and show a simple new proof due to Ravi et al for Jain's 2 approximation for Steiner network.
Connectivity
laminar
uncrossing
Mader's Theorem
power problems
1-0
Regular Paper
Guy
Kortsarz
Guy Kortsarz
Zeev
Nutov
Zeev Nutov
10.4230/DagSemProc.09511.4
Creative Commons Attribution 4.0 International license
https://creativecommons.org/licenses/by/4.0/legalcode
Contraction Bidimensionality: the Accurate Picture
We provide new combinatorial theorems on the structure of graphs that are contained as contractions in graphs of large treewidth. As a consequence of our combinatorial results we unify and significantly simplify contraction bidimensionality theory – the meta algorithmic framework to design efficient parameterized and approximation algorithms for contraction closed parameters.
Paramerterized Algorithms
Bidimensionality
Graph Minors
1-12
Regular Paper
Fedor V.
Fomin
Fedor V. Fomin
Petr
Golovach
Petr Golovach
Dimitrios M.
Thilikos
Dimitrios M. Thilikos
10.4230/DagSemProc.09511.5
Creative Commons Attribution 4.0 International license
https://creativecommons.org/licenses/by/4.0/legalcode
Differentially Private Combinatorial Optimization
Consider the following problem: given a metric space, some of whose points are ``clients,'' select a set of at most $k$ facility locations to minimize the average distance from the clients to their nearest facility. This is just the well-studied $k$-median problem, for which many approximation algorithms and hardness results are known. Note that the objective function encourages opening facilities in areas where there are many clients, and given a solution, it is often possible to get a good idea of where the clients are located. This raises the following quandary: what if the locations of the clients are sensitive information that we would like to keep private? emph{Is it even possible to design good algorithms for this problem that preserve the privacy of the clients?}
In this paper, we initiate a systematic study of algorithms for discrete optimization problems in the framework of differential privacy (which formalizes the idea of protecting the privacy of individual input elements). We show that many such problems indeed have good approximation algorithms that preserve differential privacy; this is even in cases where it is impossible to preserve cryptographic definitions of privacy while computing any non-trivial approximation to even the emph{value} of an optimal solution, let alone the entire solution.
Apart from the $k$-median problem, we consider the problems of vertex and set cover, min-cut, facility location, and Steiner tree, and give approximation algorithms and lower bounds for these problems. We also consider the recently introduced submodular maximization problem, ``Combinatorial Public Projects'' (CPP), shown by Papadimitriou et al. cite{PSS08} to be inapproximable to subpolynomial multiplicative factors by any efficient and emph{truthful} algorithm. We give a differentially private (and hence approximately truthful) algorithm that achieves a logarithmic additive approximation.
Joint work with Anupam Gupta, Katrina Ligett, Frank McSherry and Aaron Roth.
Differential Privacy
Approximation Algorithms
1-31
Regular Paper
Kunal
Talwar
Kunal Talwar
Anupam
Gupta
Anupam Gupta
Katrina
Ligett
Katrina Ligett
Frank
McSherry
Frank McSherry
Aaron
Roth
Aaron Roth
10.4230/DagSemProc.09511.6
Creative Commons Attribution 4.0 International license
https://creativecommons.org/licenses/by/4.0/legalcode
Satisfiability Allows No Nontrivial Sparsification Unless The Polynomial-Time Hierarchy Collapses
Consider the following two-player communication process to decide a
language $L$: The first player holds the entire input $x$ but is
polynomially bounded; the second player is computationally unbounded
but does not know any part of $x$; their goal is to cooperatively
decide whether $x$ belongs to $L$ at small cost, where the cost
measure is the number of bits of communication from the first player
to the second player.
For any integer $d geq 3$ and positive real $epsilon$ we show that
if satisfiability for $n$-variable $d$-CNF formulas has a protocol of
cost $O(n^{d-epsilon})$ then coNP is in NP/poly, which implies that
the polynomial-time hierarchy collapses to its third level. The result
even holds when the first player is conondeterministic, and is tight as
there exists a trivial protocol for $epsilon = 0$. Under the
hypothesis that coNP is not in NP/poly, our result implies tight lower
bounds for parameters of interest in several areas, namely
sparsification, kernelization in parameterized complexity, lossy
compression, and probabilistically checkable proofs.
By reduction, similar results hold for other NP-complete problems.
For the vertex cover problem on $n$-vertex $d$-uniform hypergraphs,
the above statement holds for any integer $d geq 2$. 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
$O(k^{2-epsilon})$ edges unless coNP is in NP/poly, where $k$ denotes
the size of the deletion set. Kernels consisting of $O(k^2)$ edges are
known for several problems in the class, including vertex cover,
feedback vertex set, and bounded-degree deletion.
Sparsification
Kernelization
Parameterized Complexity
Probabilistically Checkable Proofs
Satisfiability
Vertex Cover
1-29
Regular Paper
Holger
Dell
Holger Dell
Dieter
van Melkebeek
Dieter van Melkebeek
10.4230/DagSemProc.09511.7
Creative Commons Attribution 4.0 International license
https://creativecommons.org/licenses/by/4.0/legalcode