527 research outputs found
The parameterized complexity of some geometric problems in unbounded dimension
We study the parameterized complexity of the following fundamental geometric
problems with respect to the dimension : i) Given points in \Rd,
compute their minimum enclosing cylinder. ii) Given two -point sets in
\Rd, decide whether they can be separated by two hyperplanes. iii) Given a
system of linear inequalities with variables, find a maximum-size
feasible subsystem. We show that (the decision versions of) all these problems
are W[1]-hard when parameterized by the dimension . %and hence not solvable
in time, for any computable function and constant
%(unless FPT=W[1]). Our reductions also give a -time lower bound
(under the Exponential Time Hypothesis)
Computing the Least-core and Nucleolus for Threshold Cardinality Matching Games
Cooperative games provide a framework for fair and stable profit allocation
in multi-agent systems. \emph{Core}, \emph{least-core} and \emph{nucleolus} are
such solution concepts that characterize stability of cooperation. In this
paper, we study the algorithmic issues on the least-core and nucleolus of
threshold cardinality matching games (TCMG). A TCMG is defined on a graph
and a threshold , in which the player set is and the profit of
a coalition is 1 if the size of a maximum matching in
meets or exceeds , and 0 otherwise. We first show that for a TCMG, the
problems of computing least-core value, finding and verifying least-core payoff
are all polynomial time solvable. We also provide a general characterization of
the least core for a large class of TCMG. Next, based on Gallai-Edmonds
Decomposition in matching theory, we give a concise formulation of the
nucleolus for a typical case of TCMG which the threshold equals . When
the threshold is relevant to the input size, we prove that the nucleolus
can be obtained in polynomial time in bipartite graphs and graphs with a
perfect matching
Solving generic nonarchimedean semidefinite programs using stochastic game algorithms
A general issue in computational optimization is to develop combinatorial
algorithms for semidefinite programming. We address this issue when the base
field is nonarchimedean. We provide a solution for a class of semidefinite
feasibility problems given by generic matrices. Our approach is based on
tropical geometry. It relies on tropical spectrahedra, which are defined as the
images by the valuation of nonarchimedean spectrahedra. We establish a
correspondence between generic tropical spectrahedra and zero-sum stochastic
games with perfect information. The latter have been well studied in
algorithmic game theory. This allows us to solve nonarchimedean semidefinite
feasibility problems using algorithms for stochastic games. These algorithms
are of a combinatorial nature and work for large instances.Comment: v1: 25 pages, 4 figures; v2: 27 pages, 4 figures, minor revisions +
benchmarks added; v3: 30 pages, 6 figures, generalization to non-Metzler sign
patterns + some results have been replaced by references to the companion
work arXiv:1610.0674
Challenges of infection prevention and control in Scottish long-term care facilities
Residents living in long-term care facilities (LTCFs) are at high risk of contracting healthcare-associated infections (HAIs). The unique operational and cultural characteristics of LTCFs and the currently evolving models of healthcare delivery in Scotland create great challenges for infection prevention and control (IPC). Existing literature that discusses the challenges of infection control in LTCFs focuses on operational factors within a facility and does not explore the challenges associated with higher levels of management and the lack of evidence to support IPC practices in this setting. 1-7 Here, we provide a broader view of challenges faced by LTCFs in the context of the current health and social care models in Scotland. Many of these challenges are also faced in the rest of the United Kingdom and internationally
Node-balancing by edge-increments
Suppose you are given a graph with a weight assignment
and that your objective is to modify using legal
steps such that all vertices will have the same weight, where in each legal
step you are allowed to choose an edge and increment the weights of its end
points by .
In this paper we study several variants of this problem for graphs and
hypergraphs. On the combinatorial side we show connections with fundamental
results from matching theory such as Hall's Theorem and Tutte's Theorem. On the
algorithmic side we study the computational complexity of associated decision
problems.
Our main results are a characterization of the graphs for which any initial
assignment can be balanced by edge-increments and a strongly polynomial-time
algorithm that computes a balancing sequence of increments if one exists.Comment: 10 page
Deaf, Dumb, and Chatting Robots, Enabling Distributed Computation and Fault-Tolerance Among Stigmergic Robot
We investigate ways for the exchange of information (explicit communication)
among deaf and dumb mobile robots scattered in the plane. We introduce the use
of movement-signals (analogously to flight signals and bees waggle) as a mean
to transfer messages, enabling the use of distributed algorithms among the
robots. We propose one-to-one deterministic movement protocols that implement
explicit communication. We first present protocols for synchronous robots. We
begin with a very simple coding protocol for two robots. Based on on this
protocol, we provide one-to-one communication for any system of n \geq 2 robots
equipped with observable IDs that agree on a common direction (sense of
direction). We then propose two solutions enabling one-to-one communication
among anonymous robots. Since the robots are devoid of observable IDs, both
protocols build recognition mechanisms using the (weak) capabilities offered to
the robots. The first protocol assumes that the robots agree on a common
direction and a common handedness (chirality), while the second protocol
assumes chirality only. Next, we show how the movements of robots can provide
implicit acknowledgments in asynchronous systems. We use this result to design
asynchronous one-to-one communication with two robots only. Finally, we combine
this solution with the schemes developed in synchronous settings to fit the
general case of asynchronous one-to-one communication among any number of
robots. Our protocols enable the use of distributing algorithms based on
message exchanges among swarms of Stigmergic robots. Furthermore, they provides
robots equipped with means of communication to overcome faults of their
communication device
Online unit clustering in higher dimensions
We revisit the online Unit Clustering and Unit Covering problems in higher
dimensions: Given a set of points in a metric space, that arrive one by
one, Unit Clustering asks to partition the points into the minimum number of
clusters (subsets) of diameter at most one; while Unit Covering asks to cover
all points by the minimum number of balls of unit radius. In this paper, we
work in using the norm.
We show that the competitive ratio of any online algorithm (deterministic or
randomized) for Unit Clustering must depend on the dimension . We also give
a randomized online algorithm with competitive ratio for Unit
Clustering}of integer points (i.e., points in , , under norm). We show that the competitive ratio of
any deterministic online algorithm for Unit Covering is at least . This
ratio is the best possible, as it can be attained by a simple deterministic
algorithm that assigns points to a predefined set of unit cubes. We complement
these results with some additional lower bounds for related problems in higher
dimensions.Comment: 15 pages, 4 figures. A preliminary version appeared in the
Proceedings of the 15th Workshop on Approximation and Online Algorithms (WAOA
2017
A Compact Linear Programming Relaxation for Binary Sub-modular MRF
We propose a novel compact linear programming (LP) relaxation for binary
sub-modular MRF in the context of object segmentation. Our model is obtained by
linearizing an -norm derived from the quadratic programming (QP) form of
the MRF energy. The resultant LP model contains significantly fewer variables
and constraints compared to the conventional LP relaxation of the MRF energy.
In addition, unlike QP which can produce ambiguous labels, our model can be
viewed as a quasi-total-variation minimization problem, and it can therefore
preserve the discontinuities in the labels. We further establish a relaxation
bound between our LP model and the conventional LP model. In the experiments,
we demonstrate our method for the task of interactive object segmentation. Our
LP model outperforms QP when converting the continuous labels to binary labels
using different threshold values on the entire Oxford interactive segmentation
dataset. The computational complexity of our LP is of the same order as that of
the QP, and it is significantly lower than the conventional LP relaxation
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