163 research outputs found
Cake Cutting Algorithms for Piecewise Constant and Piecewise Uniform Valuations
Cake cutting is one of the most fundamental settings in fair division and
mechanism design without money. In this paper, we consider different levels of
three fundamental goals in cake cutting: fairness, Pareto optimality, and
strategyproofness. In particular, we present robust versions of envy-freeness
and proportionality that are not only stronger than their standard
counter-parts but also have less information requirements. We then focus on
cake cutting with piecewise constant valuations and present three desirable
algorithms: CCEA (Controlled Cake Eating Algorithm), MEA (Market Equilibrium
Algorithm) and CSD (Constrained Serial Dictatorship). CCEA is polynomial-time,
robust envy-free, and non-wasteful. It relies on parametric network flows and
recent generalizations of the probabilistic serial algorithm. For the subdomain
of piecewise uniform valuations, we show that it is also group-strategyproof.
Then, we show that there exists an algorithm (MEA) that is polynomial-time,
envy-free, proportional, and Pareto optimal. MEA is based on computing a
market-based equilibrium via a convex program and relies on the results of
Reijnierse and Potters [24] and Devanur et al. [15]. Moreover, we show that MEA
and CCEA are equivalent to mechanism 1 of Chen et. al. [12] for piecewise
uniform valuations. We then present an algorithm CSD and a way to implement it
via randomization that satisfies strategyproofness in expectation, robust
proportionality, and unanimity for piecewise constant valuations. For the case
of two agents, it is robust envy-free, robust proportional, strategyproof, and
polynomial-time. Many of our results extend to more general settings in cake
cutting that allow for variable claims and initial endowments. We also show a
few impossibility results to complement our algorithms.Comment: 39 page
08261 Abstracts Collection -- Structure-Based Compression of Complex Massive Data
From June 22, 2008 to June 27, 2008 the Dagstuhl Seminar 08261 ``Structure-Based Compression of Complex Massive Data\u27\u27 was held in the International Conference and Research Center (IBFI), Schloss Dagstuhl.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available
Stable marriages and search frictions
Stable matchings are the primary solution concept for two-sided matching markets with nontransferable utility. We investigate the strategic foundations of stability in a decentralized matching market. Towards this end, we embed the standard marriage markets in a search model with random meetings. We study the limit of steady-state equilibria as exogenous frictions vanish. The main result is that convergence of equilibrium matchings to stable matchings is guaranteed if and only if there is a unique stable matching in the underlying marriage market. Whenever there are multiple stable matchings, sequences of equilibrium matchings converging to unstable, inefficient matchings can be constructed. Thus, vanishing frictions do not guarantee the stability and efficiency of decentralized marriage markets
Quantum Kolmogorov Complexity Based on Classical Descriptions
We develop a theory of the algorithmic information in bits contained in an
individual pure quantum state. This extends classical Kolmogorov complexity to
the quantum domain retaining classical descriptions. Quantum Kolmogorov
complexity coincides with the classical Kolmogorov complexity on the classical
domain. Quantum Kolmogorov complexity is upper bounded and can be effectively
approximated from above under certain conditions. With high probability a
quantum object is incompressible. Upper- and lower bounds of the quantum
complexity of multiple copies of individual pure quantum states are derived and
may shed some light on the no-cloning properties of quantum states. In the
quantum situation complexity is not sub-additive. We discuss some relations
with ``no-cloning'' and ``approximate cloning'' properties.Comment: 17 pages, LaTeX, final and extended version of quant-ph/9907035, with
corrections to the published journal version (the two displayed equations in
the right-hand column on page 2466 had the left-hand sides of the displayed
formulas erroneously interchanged
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