Martin Pál  papers
Hubie Chen,
Martin Pál.
Optimization, Games, and Quantified Constraint Satisfaction.
Summary:
Bib info:To appear in MFCS'04.

Anupam Gupta,
R. Ravi,
Martin Pál,
Amitabh Sinha.
Boosted Sampling: Approximation Algorithms for Stochastic
Optimization.
Summary: We consider the following stochastic problem:
today, we can buy
some elements (edges, facilities, vertices..) at a low price.
Tomorrow, demands will materialize, and we will need to buy some more
elements, at a much higher price, to serve those demands.
If we assume that the demands are drawn from a known probability
distribution, what set of elements should we buy today?
We give a simple but powerful framework that gives us constant approximation
algorithms for a number of problems, such as Facility Location, Steiner tree
or Vertex Cover.
Bib info: STOC 2004.

Anupam Gupta,
Amit Kumar,
Martin Pál and
Tim Roughgarden.
Approximation Via Cost Sharing: Simple
Approximations for the Multicommodity RentorBuy
Problem.
Summary:
We consider the multicommodity rentorbuy problem, in which a set of
terminal pairs is given, and the goal is to rent and buy edges so that
the terminal pairs get connected. We show a novel connection between
cost sharing and approximation algorithms, and give a general
framework in which "strict" cost shares can be used to lift an
approximation for a "buy only" problem to a corresopnding twolevel
problem. Using this framework, we give a simple 12approximation for
the multicommodity rent or buy problem.
Note: The conference paper gives a 12approximation, but a
slight refinement of the analysis (to appear in a journal version)
shows approximation guarantee of 8.
Bib info:
Proceedings of the 44th Annual IEEE Symposium on the Foundations
of Computer Science, 2003.
slides
(long version)

Martin Pál,
Éva Tardos.
Strategy Proof Mechanisms via
Primaldual Algorithms.
Summary:
We consider the problem of sharing the cost of a facility shared by
selfish users. We assume that each user has some kind of requirement
(such as being connected to a facility) and is willing to pay a
contribution towards the shared solution if this requirement is met.
Our work is motivated by a result of Moulin and Shenker that a group
strategyproof sharing mechanism is possible if we have a
crossmonotonic cost sharing function for the problem.
We give crossmonotonic cost sharing functions for two problems:
facility location and singlesink rentorbuy. Both functions are
competitive and recover a constant fraction of the cost.
Bib info:
Proceedings of the 44th Annual IEEE Symposium on the Foundations
of Computer Science, 2003.
slides
(long version)

Mohammad Mahdian,
Martin Pál.
Universal Facility Location.
Summary: We consider a facility location problem in which the
cost of the facility can be an arbitrary nondecreasing function of
the amount of demand served. We give a 8+\epsilon approximation based
on local search. This extends and improves the result on hard
capacitated facility location from FOCS'01 (below).
Bib info:
European Symposium on Algorithms, 2003.
Surprisingly, this little paper won the best student paper award.
slides

Martin Pál,
Éva Tardos and
Tom Wexler.
Facility Location with Nonuniform Hard Capacities.
Summary:
We give the first approximation algorithm for facility location
with hard capacities. That is, each facility has a certain capacity
(may be different for different facilities) and cannot serve more
demand than its capacity (opening multiple copies of a facility is not
allowed). The algorithm is based on local search and achieves
approximation guarantee of an 9+\epsilon.
Bib info:
Proceedings of the 42nd Annual IEEE Symposium on the Foundations
of Computer Science, 2001.

Alex Slivkins,
Martin Pál.
On FixedParameter Tractability of Some Routing
Problems.
Bib info:
Cornell University Technical Report
TR20021874,
2002.

Martin Pál.
Online and Offline Paging Algorithms.
Summary:
The optimal offline paging algorithm by Belady always evicts the page
that will be requested furthest in the future. It is
obviously offline in that it needs to know the sequence of future
requests  but, surprisingly, there is an online algorithm that
exactly predicts when the optimal algorithm faults (of course it
cannot guess which page the optimal algorithm evicts). We also study
online paging algorithms in models where the page request sequence is
generated by programs with nested procedure calls.
Bib info:
My "magister" thesis at Comenius University, 2000.

Ivona Bezáková,
Martin Pál.
Planar Finite Automata.
Summary:
A finite automaton can be represented by a labeled directed
graph. What happens if we require the graph to be planar?
It turns out that every regular language has a planar
nondeterministic finite automaton, although the construction requires
exponential blowup in the number of states. There are languages over
a twoletter alphabet that cannot be accepted by a deterministic
planar finite automaton.
Bib info:
Student Science Conference, Comenius University, 1999.