31,367 research outputs found
The Price of Information in Combinatorial Optimization
Consider a network design application where we wish to lay down a
minimum-cost spanning tree in a given graph; however, we only have stochastic
information about the edge costs. To learn the precise cost of any edge, we
have to conduct a study that incurs a price. Our goal is to find a spanning
tree while minimizing the disutility, which is the sum of the tree cost and the
total price that we spend on the studies. In a different application, each edge
gives a stochastic reward value. Our goal is to find a spanning tree while
maximizing the utility, which is the tree reward minus the prices that we pay.
Situations such as the above two often arise in practice where we wish to
find a good solution to an optimization problem, but we start with only some
partial knowledge about the parameters of the problem. The missing information
can be found only after paying a probing price, which we call the price of
information. What strategy should we adopt to optimize our expected
utility/disutility?
A classical example of the above setting is Weitzman's "Pandora's box"
problem where we are given probability distributions on values of
independent random variables. The goal is to choose a single variable with a
large value, but we can find the actual outcomes only after paying a price. Our
work is a generalization of this model to other combinatorial optimization
problems such as matching, set cover, facility location, and prize-collecting
Steiner tree. We give a technique that reduces such problems to their non-price
counterparts, and use it to design exact/approximation algorithms to optimize
our utility/disutility. Our techniques extend to situations where there are
additional constraints on what parameters can be probed or when we can
simultaneously probe a subset of the parameters.Comment: SODA 201
Transportation service procurement using combinatorial auctions
Thesis (M. Eng. in Logistics)--Massachusetts Institute of Technology, Engineering Systems Division, 2003.Includes bibliographical references (leaves 39-40).Auction is a mechanism of selling distinct assets that can be both physical objects and virtual objects. Examples of virtual objects are the rights to use assets like airport time slots and FCC spectrum, or to service truckload delivery routes in a transportation network. Under some situations bidding on combinations of objects can render lower total price compare with bidding the objects one at a time, and the auction that allows bidders to bid on combinations of different assets are called combinatorial auctions. With shipper being the auctioneer and carriers being the bidders, combinatorial auction has become increasingly important in the transportation service procurement domain, due to its mechanism to align shipper s procurement interest with carrier transportation service cost structure, which in turn lowers shippers total procurement cost. The thesis provides a comprehensive review of the use of conditional bidding within a transportation combinatorial auction framework. The thesis first describes the general forms of the transportation services available, and discusses the economics of motor carriers that provide LTL and TL services. It then illustrates the basic optimization technique of conditional bidding for TL service procurement and discusses the information technologies that enable the optimization-based procurement and the actual application of the method in the real world.by XiaoPing Chen.M.Eng.in Logistic
Mathematical Programming Algorithms for Spatial Cloaking
We consider a combinatorial optimization problem for spatial information
cloaking. The problem requires computing one or several disjoint arborescences on a
graph from a predetermined root or subset of candidate roots, so that the number of
vertices in the arborescences is minimized but a given threshold on the overall weight associated with the vertices in each arborescence is reached. For a single arborescence case, we solve the problem to optimality by designing a branch-and-cut exact algorithm. Then we
adapt this algorithm for the purpose of pricing out columns in an exact branch-and-price
algorithm for the multiarborescence version. We also propose a branch-and-price-based
heuristic algorithm, where branching and pricing, respectively, act as diversification and
intensification mechanisms. The heuristic consistently finds optimal or near optimal solutions within a computing time, which can be three to four orders of magnitude smaller
than that required for exact optimization. From an application point of view, our computational results are useful to calibrate the values of relevant parameters, determining the obfuscation level that is achieved
Optimal Approximation Algorithms for Multi-agent Combinatorial Problems with Discounted Price Functions
Submodular functions are an important class of functions in combinatorial
optimization which satisfy the natural properties of decreasing marginal costs.
The study of these functions has led to strong structural properties with
applications in many areas. Recently, there has been significant interest in
extending the theory of algorithms for optimizing combinatorial problems (such
as network design problem of spanning tree) over submodular functions.
Unfortunately, the lower bounds under the general class of submodular functions
are known to be very high for many of the classical problems.
In this paper, we introduce and study an important subclass of submodular
functions, which we call discounted price functions. These functions are
succinctly representable and generalize linear cost functions. In this paper we
study the following fundamental combinatorial optimization problems: Edge
Cover, Spanning Tree, Perfect Matching and Shortest Path, and obtain tight
upper and lower bounds for these problems.
The main technical contribution of this paper is designing novel adaptive
greedy algorithms for the above problems. These algorithms greedily build the
solution whist rectifying mistakes made in the previous steps
Rate of Price Discovery in Iterative Combinatorial Auctions
We study a class of iterative combinatorial auctions which can be viewed as
subgradient descent methods for the problem of pricing bundles to balance
supply and demand. We provide concrete convergence rates for auctions in this
class, bounding the number of auction rounds needed to reach clearing prices.
Our analysis allows for a variety of pricing schemes, including item, bundle,
and polynomial pricing, and the respective convergence rates confirm that more
expressive pricing schemes come at the cost of slower convergence. We consider
two models of bidder behavior. In the first model, bidders behave
stochastically according to a random utility model, which includes standard
best-response bidding as a special case. In the second model, bidders behave
arbitrarily (even adversarially), and meaningful convergence relies on properly
designed activity rules
Algorithms as Mechanisms: The Price of Anarchy of Relax-and-Round
Many algorithms that are originally designed without explicitly considering
incentive properties are later combined with simple pricing rules and used as
mechanisms. The resulting mechanisms are often natural and simple to
understand. But how good are these algorithms as mechanisms? Truthful reporting
of valuations is typically not a dominant strategy (certainly not with a
pay-your-bid, first-price rule, but it is likely not a good strategy even with
a critical value, or second-price style rule either). Our goal is to show that
a wide class of approximation algorithms yields this way mechanisms with low
Price of Anarchy.
The seminal result of Lucier and Borodin [SODA 2010] shows that combining a
greedy algorithm that is an -approximation algorithm with a
pay-your-bid payment rule yields a mechanism whose Price of Anarchy is
. In this paper we significantly extend the class of algorithms for
which such a result is available by showing that this close connection between
approximation ratio on the one hand and Price of Anarchy on the other also
holds for the design principle of relaxation and rounding provided that the
relaxation is smooth and the rounding is oblivious.
We demonstrate the far-reaching consequences of our result by showing its
implications for sparse packing integer programs, such as multi-unit auctions
and generalized matching, for the maximum traveling salesman problem, for
combinatorial auctions, and for single source unsplittable flow problems. In
all these problems our approach leads to novel simple, near-optimal mechanisms
whose Price of Anarchy either matches or beats the performance guarantees of
known mechanisms.Comment: Extended abstract appeared in Proc. of 16th ACM Conference on
Economics and Computation (EC'15
Game-theoretic Resource Allocation Methods for Device-to-Device (D2D) Communication
Device-to-device (D2D) communication underlaying cellular networks allows
mobile devices such as smartphones and tablets to use the licensed spectrum
allocated to cellular services for direct peer-to-peer transmission. D2D
communication can use either one-hop transmission (i.e., in D2D direct
communication) or multi-hop cluster-based transmission (i.e., in D2D local area
networks). The D2D devices can compete or cooperate with each other to reuse
the radio resources in D2D networks. Therefore, resource allocation and access
for D2D communication can be treated as games. The theories behind these games
provide a variety of mathematical tools to effectively model and analyze the
individual or group behaviors of D2D users. In addition, game models can
provide distributed solutions to the resource allocation problems for D2D
communication. The aim of this article is to demonstrate the applications of
game-theoretic models to study the radio resource allocation issues in D2D
communication. The article also outlines several key open research directions.Comment: Accepted. IEEE Wireless Comms Mag. 201
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