842 research outputs found
Faster Algorithms for Computing Maximal 2-Connected Subgraphs in Sparse Directed Graphs
Connectivity related concepts are of fundamental interest in graph theory.
The area has received extensive attention over four decades, but many problems
remain unsolved, especially for directed graphs. A directed graph is
2-edge-connected (resp., 2-vertex-connected) if the removal of any edge (resp.,
vertex) leaves the graph strongly connected. In this paper we present improved
algorithms for computing the maximal 2-edge- and 2-vertex-connected subgraphs
of a given directed graph. These problems were first studied more than 35 years
ago, with time algorithms for graphs with m edges and n
vertices being known since the late 1980s. In contrast, the same problems for
undirected graphs are known to be solvable in linear time. Henzinger et al.
[ICALP 2015] recently introduced time algorithms for the directed
case, thus improving the running times for dense graphs. Our new algorithms run
in time , which further improves the running times for sparse
graphs.
The notion of 2-connectivity naturally generalizes to k-connectivity for
. For constant values of k, we extend one of our algorithms to compute the
maximal k-edge-connected in time , improving again for
sparse graphs the best known algorithm by Henzinger et al. [ICALP 2015] that
runs in time.Comment: Revised version of SODA 2017 paper including details for
k-edge-connected subgraph
New Variations of the Online <em>k</em>-Canadian Traveler Problem: Uncertain Costs at Known Locations
In this chapter, we study new variations of the online k-Canadian Traveler Problem (k-CTP) in which there is an input graph with a given source node O and a destination node D. For a specified set consisting of k edges, the edge costs are unknown (we call these uncertain edges). Costs of the remaining edges are known and given. The objective is to find an online strategy such that the traveling agent finds a route from O to D with minimum total travel cost. The agent learns the cost of an uncertain edge, when she arrives at one of its end-nodes and decides on her travel path based on the discovered cost. We call this problem the online k-Canadian Traveler Problem with uncertain edges. We analyze both the single-agent and the multi-agent versions of the problem. We propose a tight lower bound on the competitive ratio of deterministic online strategies together with an optimal online strategy for the single-agent version. We consider the multi-agent version with two different objectives. We suggest lower bounds on the competitive ratio of deterministic online strategies to these two problems
Visible 100-nm-bandwidth omni-resonant imaging through a planar Fabry-P\'erot cavity
We demonstrate broadband omni-resonant imaging through a planar Fabry-P\'erot
cavity over a bandwidth of 100~nm in the visible. The omni-resonant bandwidth
exceeds the bare cavity resonant linewidth of ~nm and even its
free-spectral-range of ~nm. Rather than modifying the cavity
structure, omni-resonance is achieved by judiciously structuring the incident
field to couple to an achromatic resonance, thus enabling omni-resonant imaging
over an unprecedented bandwidth ( spectral broadening) using
coherent or incoherent light, spatially extended or localized fields, and
stationary or moving sources
Theory of space-time supermodes in planar multimode waveguides
When an optical pulse is focused into a multimode waveguide or fiber, the
energy is divided among the available guided modes. Consequently, the initially
localized intensity spreads transversely, the spatial profile undergoes rapid
variations with axial propagation, and the pulse disperses temporally.
Space-time (ST) supermodes are pulsed guided field configurations that
propagate invariantly in multimode waveguides by assigning each mode to a
prescribed wavelength. ST supermodes can be thus viewed as spectrally discrete,
guided-wave counterpart of the recently demonstrated propagation-invariant ST
wave packets in free space. The group velocity of an ST supermode is tunable
independently -- in principle -- of the waveguide structure, group-velocity
dispersion is eliminated or dramatically curtailed, and the time-averaged
intensity profile is axially invariant along the waveguide in absence of
mode-coupling. We establish here a theoretical framework for studying ST
supermodes in planar waveguides. Modal engineering allows sculpting this
axially invariant transverse intensity profile from an on-axis peak or dip
(dark beam), to a multi-peak or flat distribution. Moreover, ST supermodes can
be synthesized using spectrally incoherent light, thus paving the way to
potential applications in optical beam delivery for lighting applications
Length-weight frequency and sex ratio of crayfish, Astacus leptodactylus, in Aras Reservoir, west Azerbaijan, Iran
The length-weight frequency and sex ratio of crayfish (Astacus leptodactylus) in Aras Reservoir, was studied seasonally from spring 2008 to winter 2009. The total mean length and weight for the crayfish were 106.43±7.94mm and 35.81±10.86g, respectively. A measured 18.99% of the caught crayfish exceeded the standard commercial size (120mm) and only 16.43% of the catch weighed higher than the standard commercial weight 50 grams. The standards have been set forth by West Azerbaijan Fishery Office. Generally, the male crayfish dominated the samples. Comparisons of growth equations confirmed that the males are heavier than females with the same size. The results showed that crayfish Astacus leptodactylus has critical condition in Aras Reservoir
Quantifying early COVID-19 outbreak transmission in South Africa and exploring vaccine efficacy scenarios
The emergence and fast global spread of COVID-19 has presented one of the greatest public health challenges in modern times with no proven cure or vaccine. Africa is still early in this epidemic, therefore the extent of disease severity is not yet clear. We used a mathematical model to fit to the observed cases of COVID-19 in South Africa to estimate the basic reproductive number and critical vaccination coverage to control the disease for different hypothetical vaccine efficacy scenarios. We also estimated the percentage reduction in effective contacts due to the social distancing measures implemented. Early model estimates show that COVID-19 outbreak in South Africa had a basic reproductive number of 2.95 (95% credible interval [CrI] 2.83-3.33). A vaccine with 70% efficacy had the capacity to contain COVID-19 outbreak but at very higher vaccination coverage 94.44% (95% Crl 92.44-99.92%) with a vaccine of 100% efficacy requiring 66.10% (95% Crl 64.72-69.95%) coverage. Social distancing measures put in place have so far reduced the number of social contacts by 80.31% (95% Crl 79.76-80.85%). These findings suggest that a highly efficacious vaccine would have been required to contain COVID-19 in South Africa. Therefore, the current social distancing measures to reduce contacts will remain key in controlling the infection in the absence of vaccines and other therapeutics
Online routing and scheduling of search-and-rescue teams
We study how to allocate and route search-and-rescue (SAR) teams to areas with trapped victims in a coordinated manner after a disaster. We propose two online strategies for these time-critical decisions considering the uncertainty about the operation times required to rescue the victims and the condition of the roads that may delay the operations. First, we follow the theoretical competitive analysis approach that takes a worst-case perspective and prove lower bounds on the competitive ratio of the two variants of the defined online problem with makespan and weighted latency objectives. Then, we test the proposed online strategies and observe their good performance against the offline optimal solutions on randomly generated instances
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