4,077 research outputs found
Proximity results and faster algorithms for Integer Programming using the Steinitz Lemma
We consider integer programming problems in standard form where , and . We show that such an integer program can be solved in time , where is an upper bound on each
absolute value of an entry in . This improves upon the longstanding best
bound of Papadimitriou (1981) of , where in addition,
the absolute values of the entries of also need to be bounded by .
Our result relies on a lemma of Steinitz that states that a set of vectors in
that is contained in the unit ball of a norm and that sum up to zero can
be ordered such that all partial sums are of norm bounded by . We also use
the Steinitz lemma to show that the -distance of an optimal integer and
fractional solution, also under the presence of upper bounds on the variables,
is bounded by . Here is again an
upper bound on the absolute values of the entries of . The novel strength of
our bound is that it is independent of . We provide evidence for the
significance of our bound by applying it to general knapsack problems where we
obtain structural and algorithmic results that improve upon the recent
literature.Comment: We achieve much milder dependence of the running time on the largest
entry in $b
Stochastic Loewner evolution in multiply connected domains
We construct radial stochastic Loewner evolution in multiply connected
domains, choosing the unit disk with concentric circular slits as a family of
standard domains. The natural driving function or input is a diffusion on the
associated Teichm\"uller space. The diffusion stops when it reaches the
boundary of the Teichm\"uller space. We show that for this driving function the
family of random growing compacts has a phase transition for and
, and that it satisfies locality for .Comment: Corrected version, references adde
The Correlator Toolbox, Metrics and Moduli
We discuss the possible set of operators from various boundary conformal
field theories to build meaningful correlators that lead via a Loewner type
procedure to generalisations of SLE(). We also highlight the
necessity of moduli for a consistent kinematic description of these more
general stochastic processes. As an illustration we give a geometric derivation
of in terms of conformally invariant random growing
compact subsets of polygons. The parameters are related to the
exterior angles of the polygons. We also show that
can be generated by a Brownian motion in a gravitational background, where the
metric and the Brownian motion are coupled. The metric is obtained as the
pull-back of the Euclidean metric of a fluctuating polygon.Comment: 3 figure
Meta-Kernelization with Structural Parameters
Meta-kernelization theorems are general results that provide polynomial
kernels for large classes of parameterized problems. The known
meta-kernelization theorems, in particular the results of Bodlaender et al.
(FOCS'09) and of Fomin et al. (FOCS'10), apply to optimization problems
parameterized by solution size. We present the first meta-kernelization
theorems that use a structural parameters of the input and not the solution
size. Let C be a graph class. We define the C-cover number of a graph to be a
the smallest number of modules the vertex set can be partitioned into, such
that each module induces a subgraph that belongs to the class C. We show that
each graph problem that can be expressed in Monadic Second Order (MSO) logic
has a polynomial kernel with a linear number of vertices when parameterized by
the C-cover number for any fixed class C of bounded rank-width (or
equivalently, of bounded clique-width, or bounded Boolean width). Many graph
problems such as Independent Dominating Set, c-Coloring, and c-Domatic Number
are covered by this meta-kernelization result. Our second result applies to MSO
expressible optimization problems, such as Minimum Vertex Cover, Minimum
Dominating Set, and Maximum Clique. We show that these problems admit a
polynomial annotated kernel with a linear number of vertices
On the Rigidity Theorem for Spacetimes with a Stationary Event Horizon or a Compact Cauchy Horizon
We consider smooth electrovac spacetimes which represent either (A) an
asymptotically flat, stationary black hole or (B) a cosmological spacetime with
a compact Cauchy horizon ruled by closed null geodesics. The black hole event
horizon or, respectively, the compact Cauchy horizon of these spacetimes is
assumed to be a smooth null hypersurface which is non-degenerate in the sense
that its null geodesic generators are geodesically incomplete in one direction.
In both cases, it is shown that there exists a Killing vector field in a
one-sided neighborhood of the horizon which is normal to the horizon. We
thereby generalize theorems of Hawking (for case (A)) and Isenberg and Moncrief
(for case (B)) to the non-analytic case.Comment: 16 pages, no figure
Incentive Design and Trust: Comparing the Effects of Tournament and Team-Based Incentives on Trust
We explore the extent to which the structure of incentives affects trust. We hypothesize that the degree to which different incentive mechanisms emphasize competition (via the perceived intentions of others) and entitlements (via the perceived property rights) will affect individuals’ subsequent behavior. In our experiment, bargaining pairs earned endowments through either tournaments or team-based incentives. Participants engaged in a subsequent trust game in which the sender had access to the total endowment generated by the pair. We find that the structure of the incentive mechanisms has asymmetric effects on observed trust in which participants’ relative performance framed trusting behavior.trust, incentives, experiments, tournaments
A Note on Non-Degenerate Integer Programs with Small Sub-Determinants
The intention of this note is two-fold. First, we study integer optimization
problems in standard form defined by and present
an algorithm to solve such problems in polynomial-time provided that both the
largest absolute value of an entry in and are constant. Then, this is
applied to solve integer programs in inequality form in polynomial-time, where
the absolute values of all maximal sub-determinants of lie between and
a constant
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