333 research outputs found
Constant-factor approximations for Capacitated Arc Routing without triangle inequality
Given an undirected graph with edge costs and edge demands, the Capacitated
Arc Routing problem (CARP) asks for minimum-cost routes for equal-capacity
vehicles so as to satisfy all demands. Constant-factor polynomial-time
approximation algorithms were proposed for CARP with triangle inequality, while
CARP was claimed to be NP-hard to approximate within any constant factor in
general. Correcting this claim, we show that any factor {\alpha} approximation
for CARP with triangle inequality yields a factor {\alpha} approximation for
the general CARP
Asymptotic constant-factor approximation algorithm for the Traveling Salesperson Problem for Dubins' vehicle
This article proposes the first known algorithm that achieves a
constant-factor approximation of the minimum length tour for a Dubins' vehicle
through points on the plane. By Dubins' vehicle, we mean a vehicle
constrained to move at constant speed along paths with bounded curvature
without reversing direction. For this version of the classic Traveling
Salesperson Problem, our algorithm closes the gap between previously
established lower and upper bounds; the achievable performance is of order
Greedy MAXCUT Algorithms and their Information Content
MAXCUT defines a classical NP-hard problem for graph partitioning and it
serves as a typical case of the symmetric non-monotone Unconstrained Submodular
Maximization (USM) problem. Applications of MAXCUT are abundant in machine
learning, computer vision and statistical physics. Greedy algorithms to
approximately solve MAXCUT rely on greedy vertex labelling or on an edge
contraction strategy. These algorithms have been studied by measuring their
approximation ratios in the worst case setting but very little is known to
characterize their robustness to noise contaminations of the input data in the
average case. Adapting the framework of Approximation Set Coding, we present a
method to exactly measure the cardinality of the algorithmic approximation sets
of five greedy MAXCUT algorithms. Their information contents are explored for
graph instances generated by two different noise models: the edge reversal
model and Gaussian edge weights model. The results provide insights into the
robustness of different greedy heuristics and techniques for MAXCUT, which can
be used for algorithm design of general USM problems.Comment: This is a longer version of the paper published in 2015 IEEE
Information Theory Workshop (ITW
Progress on pricing with peering
This paper examines a simple model of how a
provider ISP charges customer ISPs by assuming the provider
ISP wants to maximize its revenue when customer ISPs have
the possibility of setting up peering connections. It is shown that
finding the optimal pricing is NP-complete, and APX-complete.
Customers can respond to price in many ways, including throttling
traffic as well as peering. An algorithm is studied which
obtains a 1/4 approximation for a wide range of customer
responses
Approximating the Regular Graphic TSP in near linear time
We present a randomized approximation algorithm for computing traveling
salesperson tours in undirected regular graphs. Given an -vertex,
-regular graph, the algorithm computes a tour of length at most
, with high probability, in time. This improves upon a recent result by Vishnoi (\cite{Vishnoi12}, FOCS
2012) for the same problem, in terms of both approximation factor, and running
time. The key ingredient of our algorithm is a technique that uses
edge-coloring algorithms to sample a cycle cover with cycles with
high probability, in near linear time.
Additionally, we also give a deterministic
factor approximation algorithm
running in time .Comment: 12 page
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