Seminář z aproximačních a online algoritmů
Seminar on Approximation and Online Algorithms

Andreas Emil Feldmann, Petr Kolman, Jiří Sgall

Doba a místo konání [Time and place]

UMLUVENO: V ZS 2017 se koná v pátek od 10:40 v posluchárně S6

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Kontakt, tel. 951 554 372;, tel. 951 554 155;, tel. 951 554 293.

Nejbližší program semináře [Next program]

20. 10. 2017 (pátek [Friday], 10:40, MFF UK Malá Strana S6)

Pavel Veselý: Parameterized Approximation Schemes for Steiner Trees with Small Number of Steiner Vertices
(continued; joint work with Pavel Dvořák, Andreas Emil Feldmann, Dušan Knop, Tomáš Masařík, and Tomáš Toufar)

We study the Steiner Tree problem, in which a set of terminal vertices needs to be connected in the cheapest possible way in an edge-weighted graph. This probl em has been extensively studied from the viewpoint of approximation and also parametrization. In particular, on one hand Steiner Tree is known to be APX- hard, and W[2]-hard on the other, if parameterized by the number of non-terminals (Steiner vertices) in the optimum solution. In contrast to this we give an efficient parameterized approximation scheme (EPAS), which circumvents both hardness results. Moreover, our methods imply the existence of a polynomial size approximate kernelization scheme (PSAKS) for the assumed p arameter.

We further study the parameterized approximability of other variants of Steiner Tree, such as Directed Steiner Tree and Steiner Forest. For neither of these an EPTAS is likely to exist for the studied parameter: for Steiner Forest an easy observation shows that the problem is APX-hard, even if the input graph contains no Steiner vertices. For Directed Steiner Tree we prove that computing a constant approximation for this parameter is W[1]- hard. Nevertheless, we show that an EPAS exists for Unweighted Directed Steiner Tree. Also we prove that there is an EPAS and a PSAKS for Steiner Forest if in addition to the number of Steiner vertices, the number of connected components of an optimal solution is considered to be a parameter.

Předběžný další program [Preliminary future program]

Martin Skutella: A Note on the Ring Loading Problem. SIAM J. Discrete Math., 30(1), 327-342. 2016.
(presented by Lukáš Folwarczný)

Ola Svensson, Jakub Tarnawski, László A. Végh: A Constant-Factor Approximation Algorithm for the Asymmetric Traveling Salesman Problem.
(presented by Pavel Veselý)

Syamantak Das and Andreas Wiese. On minimizing the makespan when some jobs cannot be assigned on the same machine. ESA 2017.
(presented by Jan Voborník)

Moses Charikar, Konstantin Makarychev, Yury Makarychev: Integrality Gaps for Sherali-Adams Relaxations. STOC 2009.
(presented by Jakub Sosnovec)

Další články pro ZS 2017 [More papers proposed for this semester]

Euiwoong Lee: Improved Hardness for Cut, Interdiction, and Firefighter Problems. ICALP 2017. Best Student Paper. Also

Andreas Wiese: A (1+eps)-approximation for Unsplittable Flow on a Path in fixed-parameter running time. ICALP 2017.

Parinya Chalermsook, Marek Cygan, Guy Kortsarz, Bundit Laekhanukit, Pasin Manurangsi, Danupon Nanongkai, Luca Trevisan: From Gap-ETH to FPT-Inapproximability: Clique, Dominating Set, and More. FOCS 2017. Also

Michael Lampis: Parameterized Approximation Schemes using Graph Widths. ICALP 2014. Also

Alice Paul, Daniel Freund, Aaron Ferber, David Shmoys and David Williamson: Prize-Collecting TSP with a Budget Constraint. ESA 2017.

Samozřejmě, jako vždy, jsou vítany jsou i další náměty, zejména pak prezentace vlastních výsledků účastníků semináře.

Další články, o kterých jsme uvažovali, zbylé z minulého semestru atd.
[Additional proposed papers, leftovers from the last semester]

Klaus Jansen and Lars Rohwedder: On the Configuration-LP of the Restricted Assignment Problem. SODA 2017: 2670-2678, also

Martijn van Ee, Leo van Iersel, Teun Janssen, René Sitters: A priori TSP in the Scenario Model. WAOA 2016: 183-196.

Alantha Newman, Heiko Röglin, and Johanna Seif: The Alternating Stock Size Problem and the Gasoline Puzzle. ESA 2016. Also

János Balogh, József Békési, György Dósa, Leah Epstein, Asaf Levin: Online bin packing with cardinality constraints resolved. At

Harald Räcke: Optimal hierarchical decompositions for congestion minimization in networks. STOC 2008:255-264. Also here.

Jittat Fakcheroenphol, Kunal Talwar and Satish Rao: A tight bound on approximating arbitrary metrics by tree metrics. STOC 2003, J. Comput. Syst. Sci. 69(3): 485-497 (2004).

Předchozí program semináře [Past program]