1,100 research outputs found
Automatic differentiation of non-holonomic fast marching for computing most threatening trajectories under sensors surveillance
We consider a two player game, where a first player has to install a
surveillance system within an admissible region. The second player needs to
enter the the monitored area, visit a target region, and then leave the area,
while minimizing his overall probability of detection. Both players know the
target region, and the second player knows the surveillance installation
details.Optimal trajectories for the second player are computed using a
recently developed variant of the fast marching algorithm, which takes into
account curvature constraints modeling the second player vehicle
maneuverability. The surveillance system optimization leverages a reverse-mode
semi-automatic differentiation procedure, estimating the gradient of the value
function related to the sensor location in time N log N
Three-manifolds, Foliations and Circles, I
This paper investigates certain foliations of three-manifolds that are
hybrids of fibrations over the circle with foliated circle bundles over
surfaces: a 3-manifold slithers around the circle when its universal cover
fibers over the circle so that deck transformations are bundle automorphisms.
Examples include hyperbolic 3-manifolds of every possible homological type. We
show that all such foliations admit transverse pseudo-Anosov flows, and that in
the universal cover of the hyperbolic cases, the leaves limit to sphere-filling
Peano curves. The skew R-covered Anosov foliations of Sergio Fenley are
examples. We hope later to use this structure for geometrization of slithered
3-manifolds.Comment: 60 pages, 10 figure
The Good, the Bad and the Submodular: Fairly Allocating Mixed Manna Under Order-Neutral Submodular Preferences
We study the problem of fairly allocating indivisible goods (positively
valued items) and chores (negatively valued items) among agents with decreasing
marginal utilities over items. Our focus is on instances where all the agents
have simple preferences; specifically, we assume the marginal value of an item
can be either , or some positive integer . Under this assumption, we
present an efficient algorithm to compute leximin allocations for a broad class
of valuation functions we call order-neutral submodular valuations.
Order-neutral submodular valuations strictly contain the well-studied class of
additive valuations but are a strict subset of the class of submodular
valuations. We show that these leximin allocations are Lorenz dominating and
approximately proportional. We also show that, under further restriction to
additive valuations, these leximin allocations are approximately envy-free and
guarantee each agent their maxmin share. We complement this algorithmic result
with a lower bound showing that the problem of computing leximin allocations is
NP-hard when is a rational number
Near-Optimal Decremental SSSP in Dense Weighted Digraphs
In the decremental Single-Source Shortest Path problem (SSSP), we are given a
weighted directed graph undergoing edge deletions and a source
vertex ; let and be the aspect ratio of the
graph. The goal is to obtain a data structure that maintains shortest paths
from to all vertices in and can answer distance queries in time,
as well as return the corresponding path in time.
This problem was first considered by Even and Shiloach [JACM'81], who
provided an algorithm with total update time for unweighted undirected
graphs; this was later extended to directed weighted graphs [FOCS'95, STOC'99].
There are conditional lower bounds showing that is in fact near-optimal
[ESA'04, FOCS'14, STOC'15, STOC'20]. In a breakthrough result, Forster et al.
showed that it is possible to achieve total update time
if the algorithm is allowed to return -approximate paths,
instead of exact ones [STOC'14, ICALP'15]. No further progress was made until
Probst Gutenberg and Wulff-Nilsen [SODA'20] provided a new approach for the
problem, which yields total time .
Our result builds on this recent approach, but overcomes its limitations by
introducing a significantly more powerful abstraction, as well as a different
core subroutine. Our new framework yields a decremental
-approximate SSSP data structure with total update time
. Our algorithm is thus near-optimal for dense graphs
with polynomial edge-weights. Our framework can also be applied to sparse
graphs to obtain total update time .
Our main technique allows us to convert SSSP algorithms for DAGs to ones for
general graphs, which we believe has significant potential to influence future
work.Comment: Accepted to FOCS'2
Do Prices Coordinate Markets?
Walrasian equilibrium prices can be said to coordinate markets: They support
a welfare optimal allocation in which each buyer is buying bundle of goods that
is individually most preferred. However, this clean story has two caveats.
First, the prices alone are not sufficient to coordinate the market, and buyers
may need to select among their most preferred bundles in a coordinated way to
find a feasible allocation. Second, we don't in practice expect to encounter
exact equilibrium prices tailored to the market, but instead only approximate
prices, somehow encoding "distributional" information about the market. How
well do prices work to coordinate markets when tie-breaking is not coordinated,
and they encode only distributional information?
We answer this question. First, we provide a genericity condition such that
for buyers with Matroid Based Valuations, overdemand with respect to
equilibrium prices is at most 1, independent of the supply of goods, even when
tie-breaking is done in an uncoordinated fashion. Second, we provide
learning-theoretic results that show that such prices are robust to changing
the buyers in the market, so long as all buyers are sampled from the same
(unknown) distribution
Winding Roads: Routing edges into bundles
International audienceVisualizing graphs containing many nodes and edges efficiently is quite challenging. Drawings of such graphs generally suffer from visual clutter induced by the large amount of edges and their crossings. Consequently, it is difficult to read the relationships between nodes and the high-level edge patterns that may exist in standard node- link diagram representations. Edge bundling techniques have been proposed to help solve this issue, which rely on high quality edge rerouting. In this paper, we introduce an intuitive edge bundling technique which efficiently reduces edge clutter in graphs drawings. Our method is based on the use of a grid built using the original graph to compute the edge rerouting. In comparison with previously proposed edge bundling methods, our technique improves both the level of clutter reduction and the computation performance. The second contribution of this paper is a GPU-based rendering method which helps users perceive bundles densities while preserving edge color
10211 Abstracts Collection -- Flexible Network Design
From Monday 24.05.2010---Friday 28.05.2010, the Dagstuhl Seminar 10211 ``Flexible Network Design \u27\u27 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
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