128,203 research outputs found
Optimal Fair Computation
A computation scheme among n parties is fair if no party obtains the computation result unless all other n-1 parties obtain the same result. A fair computation scheme is optimistic if n honest parties can obtain the computation result without resorting to a trusted third party. We prove, for the first time, a tight lower bound on the message complexity of optimistic fair computation for n parties among which n-1 can be malicious in an asynchronous network. We do so by relating the optimal message complexity of optimistic fair computation to the length of the shortest permutation sequence in combinatorics
Fair Bandwidth Allocation for Multicasting in Networks with Discrete Feasible Set
We study fairness in allocating bandwidth for loss-tolerant real-time multicast applications. We assume that the traffic is encoded in several layers so that the network can adapt to the available bandwidth and receiver processing capabilities by varying the number of layers delivered. We consider the case where receivers cannot subscribe to fractional layers. Therefore, the network can allocate only a discrete set of bandwidth to a receiver, whereas a continuous set of rates can be allocated when receivers can subscribe to fractional layers. Fairness issues differ vastly in these two different cases. Computation of lexicographic optimal rate allocation becomes NP-hard in this case, while lexicographic optimal rate allocation is polynomial complexity computable when fractional layers can be allocated. Furthermore, maxmin fair rate vector may not exist in this case. We introduce a new notion of fairness, maximal fairness. Even though maximal fairness is a weaker notion of fairness, it has many intuitively appealing fairness properties. For example, it coincides with lexicographic optimality and maxmin fairness, when maxmin fair rate allocation exists. We propose a polynomial complexity algorithm for computation of maximally fair rates allocated to various source-destination pairs, which incidentally computes the maxmin fair rate allocation, when the latter exists
Polynomial-Time Space-Optimal Silent Self-Stabilizing Minimum-Degree Spanning Tree Construction
Motivated by applications to sensor networks, as well as to many other areas,
this paper studies the construction of minimum-degree spanning trees. We
consider the classical node-register state model, with a weakly fair scheduler,
and we present a space-optimal \emph{silent} self-stabilizing construction of
minimum-degree spanning trees in this model. Computing a spanning tree with
minimum degree is NP-hard. Therefore, we actually focus on constructing a
spanning tree whose degree is within one from the optimal. Our algorithm uses
registers on bits, converges in a polynomial number of rounds, and
performs polynomial-time computation at each node. Specifically, the algorithm
constructs and stabilizes on a special class of spanning trees, with degree at
most . Indeed, we prove that, unless NP coNP, there are no
proof-labeling schemes involving polynomial-time computation at each node for
the whole family of spanning trees with degree at most . Up to our
knowledge, this is the first example of the design of a compact silent
self-stabilizing algorithm constructing, and stabilizing on a subset of optimal
solutions to a natural problem for which there are no time-efficient
proof-labeling schemes. On our way to design our algorithm, we establish a set
of independent results that may have interest on their own. In particular, we
describe a new space-optimal silent self-stabilizing spanning tree
construction, stabilizing on \emph{any} spanning tree, in rounds, and
using just \emph{one} additional bit compared to the size of the labels used to
certify trees. We also design a silent loop-free self-stabilizing algorithm for
transforming a tree into another tree. Last but not least, we provide a silent
self-stabilizing algorithm for computing and certifying the labels of a
NCA-labeling scheme
Routing Games with Progressive Filling
Max-min fairness (MMF) is a widely known approach to a fair allocation of
bandwidth to each of the users in a network. This allocation can be computed by
uniformly raising the bandwidths of all users without violating capacity
constraints. We consider an extension of these allocations by raising the
bandwidth with arbitrary and not necessarily uniform time-depending velocities
(allocation rates). These allocations are used in a game-theoretic context for
routing choices, which we formalize in progressive filling games (PFGs).
We present a variety of results for equilibria in PFGs. We show that these
games possess pure Nash and strong equilibria. While computation in general is
NP-hard, there are polynomial-time algorithms for prominent classes of
Max-Min-Fair Games (MMFG), including the case when all users have the same
source-destination pair. We characterize prices of anarchy and stability for
pure Nash and strong equilibria in PFGs and MMFGs when players have different
or the same source-destination pairs. In addition, we show that when a designer
can adjust allocation rates, it is possible to design games with optimal strong
equilibria. Some initial results on polynomial-time algorithms in this
direction are also derived
Fair Interventions in Weighted Congestion Games
In this work we study the power and limitations of fair interventions in
weighted congestion games. Specifically, we focus on interventions that aim at
improving the equilibrium quality (price of anarchy) and are fair in the sense
that identical players receive identical treatment. Within this setting, we
provide three key contributions: First, we show that no fair intervention can
reduce the price of anarchy below a given factor depending solely on the class
of latencies considered. Interestingly, this lower bound is unconditional,
i.e., it applies regardless of how much computation interventions are allowed
to use. Second, we propose a taxation mechanism that is fair and show that the
resulting price of anarchy matches this lower bound, while the mechanism can be
efficiently computed in polynomial time. Third, we complement these results by
showing that no intervention (fair or not) can achieve a better approximation
if polynomial computability is required. We do so by proving that the minimum
social cost is NP-hard to approximate below a factor identical to the one
previously introduced. In doing so, we also show that the randomized algorithm
proposed by Makarychev and Sviridenko (Journal of the ACM, 2018) for the class
of optimization problems with a "diseconomy of scale" is optimal, and provide a
novel way to derandomize its solution via equilibrium computation
Fair Data Representation for Machine Learning at the Pareto Frontier
As machine learning powered decision making is playing an increasingly
important role in our daily lives, it is imperative to strive for fairness of
the underlying data processing and algorithms. We propose a pre-processing
algorithm for fair data representation via which L2- objective supervised
learning algorithms result in an estimation of the Pareto frontier between
prediction error and statistical disparity. In particular, the present work
applies the optimal positive definite affine transport maps to approach the
post-processing Wasserstein barycenter characterization of the optimal fair
L2-objective supervised learning via a pre-processing data deformation. We call
the resulting data Wasserstein pseudo-barycenter. Furthermore, we show that the
Wasserstein geodesics from the learning outcome marginals to the barycenter
characterizes the Pareto frontier between L2-loss and total Wasserstein
distance among learning outcome marginals. Thereby, an application of McCann
interpolation generalizes the pseudo-barycenter to a family of data
representations via which L2-objective supervised learning algorithms result in
the Pareto frontier. Numerical simulations underscore the advantages of the
proposed data representation: (1) the pre-processing step is compositive with
arbitrary L2-objective supervised learning methods and unseen data; (2) the
fair representation protects data privacy by preventing the training machine
from direct or indirect access to the sensitive information of the data; (3)
the optimal affine map results in efficient computation of fair supervised
learning on high-dimensional data; (4) experimental results shed light on the
fairness of L2-objective unsupervised learning via the proposed fair data
representation.Comment: 57 pages, 9 figure
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