5,590 research outputs found
Approximating Generalized Network Design under (Dis)economies of Scale with Applications to Energy Efficiency
In a generalized network design (GND) problem, a set of resources are
assigned to multiple communication requests. Each request contributes its
weight to the resources it uses and the total load on a resource is then
translated to the cost it incurs via a resource specific cost function. For
example, a request may be to establish a virtual circuit, thus contributing to
the load on each edge in the circuit. Motivated by energy efficiency
applications, recently, there is a growing interest in GND using cost functions
that exhibit (dis)economies of scale ((D)oS), namely, cost functions that
appear subadditive for small loads and superadditive for larger loads.
The current paper advances the existing literature on approximation
algorithms for GND problems with (D)oS cost functions in various aspects: (1)
we present a generic approximation framework that yields approximation results
for a much wider family of requests in both directed and undirected graphs; (2)
our framework allows for unrelated weights, thus providing the first
non-trivial approximation for the problem of scheduling unrelated parallel
machines with (D)oS cost functions; (3) our framework is fully combinatorial
and runs in strongly polynomial time; (4) the family of (D)oS cost functions
considered in the current paper is more general than the one considered in the
existing literature, providing a more accurate abstraction for practical energy
conservation scenarios; and (5) we obtain the first approximation ratio for GND
with (D)oS cost functions that depends only on the parameters of the resources'
technology and does not grow with the number of resources, the number of
requests, or their weights. The design of our framework relies heavily on
Roughgarden's smoothness toolbox (JACM 2015), thus demonstrating the possible
usefulness of this toolbox in the area of approximation algorithms.Comment: 39 pages, 1 figure. An extended abstract of this paper is to appear
in the 50th Annual ACM Symposium on the Theory of Computing (STOC 2018
Game theoretic controller synthesis for multi-robot motion planning Part I : Trajectory based algorithms
We consider a class of multi-robot motion planning problems where each robot
is associated with multiple objectives and decoupled task specifications. The
problems are formulated as an open-loop non-cooperative differential game. A
distributed anytime algorithm is proposed to compute a Nash equilibrium of the
game. The following properties are proven: (i) the algorithm asymptotically
converges to the set of Nash equilibrium; (ii) for scalar cost functionals, the
price of stability equals one; (iii) for the worst case, the computational
complexity and communication cost are linear in the robot number
Probability Distributions on Partially Ordered Sets and Network Interdiction Games
This article poses the following problem: Does there exist a probability
distribution over subsets of a finite partially ordered set (poset), such that
a set of constraints involving marginal probabilities of the poset's elements
and maximal chains is satisfied? We present a combinatorial algorithm to
positively resolve this question. The algorithm can be implemented in
polynomial time in the special case where maximal chain probabilities are
affine functions of their elements. This existence problem is relevant for the
equilibrium characterization of a generic strategic interdiction game on a
capacitated flow network. The game involves a routing entity that sends its
flow through the network while facing path transportation costs, and an
interdictor who simultaneously interdicts one or more edges while facing edge
interdiction costs. Using our existence result on posets and strict
complementary slackness in linear programming, we show that the Nash equilibria
of this game can be fully described using primal and dual solutions of a
minimum-cost circulation problem. Our analysis provides a new characterization
of the critical components in the interdiction game. It also leads to a
polynomial-time approach for equilibrium computation
A Comprehensive Survey of Potential Game Approaches to Wireless Networks
Potential games form a class of non-cooperative games where unilateral
improvement dynamics are guaranteed to converge in many practical cases. The
potential game approach has been applied to a wide range of wireless network
problems, particularly to a variety of channel assignment problems. In this
paper, the properties of potential games are introduced, and games in wireless
networks that have been proven to be potential games are comprehensively
discussed.Comment: 44 pages, 6 figures, to appear in IEICE Transactions on
Communications, vol. E98-B, no. 9, Sept. 201
Pricing Network Edges to Cross a River.
We consider a Stackelberg pricing problem in directed networks:Tariffs (prices) have to be defined by an operator, the leader, for a subset of the arcs. Clients, the followers, choose paths to route their demand through the network selfishly and independently of each other, on the basis of minimal total cost. The problem is to find tariffs such as to maximize the operator''s revenue. We consider the case where each client takes at most one tariff arc to route the demand.The problem, which we refer to as the river tarification problem, is a special case of problems studied previously in the literature.We prove that the problem is strongly NP-hard.Moreover, we show that the polynomially solvable case of uniform tarification yields an m--approximation algorithm, and this is tight. We suggest a new type of analysis that allows to improve the result to \bigO{\log m}, whenever the input data is polynomially bounded. We furthermore derive an \bigO{m^{1-\varepsilon}}--inapproximability result for problems where the operator must serve all clients, and we discuss some polynomial special cases. Finally, a computational study with instances from France Telecom suggests that uniform pricing performs better in practice than theory would suggest.operations research and management science;
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