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Approximating k-median via pseudo-approximation
We present a novel approximation algorithm for k-median that achieves an approximation guarantee of 1+√3+ε, improving upon the decade-old ratio of 3+ε. Our approach is based on two components, each
Approximating Graphic TSP by Matchings
TLDR
A framework for approximating the metric TSP based on a novel use of matchings that allows for generalizations in a natural way and also leads to a 1.586-approximation algorithm for the traveling salesman path problem on graphic metrics where the start and end vertices are prespecified.
Online Contention Resolution Schemes
TLDR
A new rounding technique designed for online optimization problems, which is related to contention resolution schemes, a technique initially introduced in the context of submodular function maximization, and the first constant-factor algorithm for weighted stochastic probing with deadlines are introduced.
Better Guarantees for k-Means and Euclidean k-Median by Primal-Dual Algorithms
TLDR
A new primal-dual approach is presented that allows to exploit the geometric structure of k-means and to satisfy the hard constraint that at most k clusters are selected without deteriorating the approximation guarantee.
The influence of multiple introduced predators on a littoral pond community
TLDR
It is demonstrated that noninteracting, introduced multiple predators can have strong direct and indirect effects on multiple trophic levels in pond communities, andTrophic cascades may develop in aquatic food webs even with omnivores such as crayfish, and in complex habitats with trout.
Centrality of Trees for Capacitated k-Center
TLDR
Evidence is given to show that more powerful preprocessing could lead to better algorithms, by giving an approximation algorithm that beats the integrality gap for instances where all non-zero capacities are the same.
Santa Claus schedules jobs on unrelated machines
TLDR
The main result is a polynomial time algorithm that estimates the optimal makespan of the restricted assignment problem within a factor 33/17 + ε ~ 1.9412 +ε, where ε > 0 is an arbitrarily small constant.
Parental behaviour in relation to food availability in the common goby
TLDR
There was an association between how well the nest was built and partial clutch filial cannibalism, suggesting that the appearance of the nest may indicate the condition of the male, and thus the risk of filial Cannibalism.
LP-Based Algorithms for Capacitated Facility Location
TLDR
A linear programming relaxation with constant integrality gap for capacitated facility location is presented and it is demonstrated that the fundamental theories of multi-commodity flows and matchings provide key insights that lead to the strong relaxation.
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