1,984 research outputs found
Improved approximation for 3-dimensional matching via bounded pathwidth local search
One of the most natural optimization problems is the k-Set Packing problem,
where given a family of sets of size at most k one should select a maximum size
subfamily of pairwise disjoint sets. A special case of 3-Set Packing is the
well known 3-Dimensional Matching problem. Both problems belong to the Karp`s
list of 21 NP-complete problems. The best known polynomial time approximation
ratio for k-Set Packing is (k + eps)/2 and goes back to the work of Hurkens and
Schrijver [SIDMA`89], which gives (1.5 + eps)-approximation for 3-Dimensional
Matching. Those results are obtained by a simple local search algorithm, that
uses constant size swaps.
The main result of the paper is a new approach to local search for k-Set
Packing where only a special type of swaps is considered, which we call swaps
of bounded pathwidth. We show that for a fixed value of k one can search the
space of r-size swaps of constant pathwidth in c^r poly(|F|) time. Moreover we
present an analysis proving that a local search maximum with respect to O(log
|F|)-size swaps of constant pathwidth yields a polynomial time (k + 1 +
eps)/3-approximation algorithm, improving the best known approximation ratio
for k-Set Packing. In particular we improve the approximation ratio for
3-Dimensional Matching from 3/2 + eps to 4/3 + eps.Comment: To appear in proceedings of FOCS 201
Between here and there: Immigrant fertility patterns in Germany
This paper focuses on the role of the home country’s birth rates in shaping immigrant fertility. We use the German Socio-Economic Panel (SOEP) to study completed fertility of first generation immigrants who arrived from different countries and at different time. We apply generalized Poisson regression to account for the underdispersion of the dependent variable. The results favor the socialization hypothesis holding that immigrants follow childbearing norms dominant in their home countries. We find that women from countries where the average birth rate is high tend to have significantly more children themselves. In addition, this relationship is the stronger, the later in life migration occurred.migration, fertility, socialization, underdispersion
Approximating Upper Degree-Constrained Partial Orientations
In the Upper Degree-Constrained Partial Orientation problem we are given an
undirected graph , together with two degree constraint functions
. The goal is to orient as many edges as possible,
in such a way that for each vertex the number of arcs entering is
at most , whereas the number of arcs leaving is at most .
This problem was introduced by Gabow [SODA'06], who proved it to be MAXSNP-hard
(and thus APX-hard). In the same paper Gabow presented an LP-based iterative
rounding -approximation algorithm.
Since the problem in question is a special case of the classic 3-Dimensional
Matching, which in turn is a special case of the -Set Packing problem, it is
reasonable to ask whether recent improvements in approximation algorithms for
the latter two problems [Cygan, FOCS'13; Sviridenko & Ward, ICALP'13] allow for
an improved approximation for Upper Degree-Constrained Partial Orientation. We
follow this line of reasoning and present a polynomial-time local search
algorithm with approximation ratio . Our algorithm uses a
combination of two types of rules: improving sets of bounded pathwidth from the
recent -approximation algorithm for 3-Set Packing [Cygan,
FOCS'13], and a simple rule tailor-made for the setting of partial
orientations. In particular, we exploit the fact that one can check in
polynomial time whether it is possible to orient all the edges of a given graph
[Gy\'arf\'as & Frank, Combinatorics'76].Comment: 12 pages, 1 figur
Alpha-stable random walk has massive thorns
We introduce and study a class of random walks defined on the integer lattice
-- a discrete space and time counterpart of the symmetric
-stable process in . When any coordinate
axis in , , is a non-massive set whereas any cone is
massive. We provide a necessary and sufficient condition for the thorn to be a
massive set.Comment: 26 pages, 2 figure
Constant Factor Approximation for Capacitated k-Center with Outliers
The -center problem is a classic facility location problem, where given an
edge-weighted graph one is to find a subset of vertices ,
such that each vertex in is "close" to some vertex in . The
approximation status of this basic problem is well understood, as a simple
2-approximation algorithm is known to be tight. Consequently different
extensions were studied.
In the capacitated version of the problem each vertex is assigned a capacity,
which is a strict upper bound on the number of clients a facility can serve,
when located at this vertex. A constant factor approximation for the
capacitated -center was obtained last year by Cygan, Hajiaghayi and Khuller
[FOCS'12], which was recently improved to a 9-approximation by An, Bhaskara and
Svensson [arXiv'13].
In a different generalization of the problem some clients (denoted as
outliers) may be disregarded. Here we are additionally given an integer and
the goal is to serve exactly clients, which the algorithm is free to
choose. In 2001 Charikar et al. [SODA'01] presented a 3-approximation for the
-center problem with outliers.
In this paper we consider a common generalization of the two extensions
previously studied separately, i.e. we work with the capacitated -center
with outliers. We present the first constant factor approximation algorithm
with approximation ratio of 25 even for the case of non-uniform hard
capacities.Comment: 15 pages, 3 figures, accepted to STACS 201
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