867 research outputs found
Sequential item pricing for unlimited supply
We investigate the extent to which price updates can increase the revenue of
a seller with little prior information on demand. We study prior-free revenue
maximization for a seller with unlimited supply of n item types facing m myopic
buyers present for k < log n days. For the static (k = 1) case, Balcan et al.
[2] show that one random item price (the same on each item) yields revenue
within a \Theta(log m + log n) factor of optimum and this factor is tight. We
define the hereditary maximizers property of buyer valuations (satisfied by any
multi-unit or gross substitutes valuation) that is sufficient for a significant
improvement of the approximation factor in the dynamic (k > 1) setting. Our
main result is a non-increasing, randomized, schedule of k equal item prices
with expected revenue within a O((log m + log n) / k) factor of optimum for
private valuations with hereditary maximizers. This factor is almost tight: we
show that any pricing scheme over k days has a revenue approximation factor of
at least (log m + log n) / (3k). We obtain analogous matching lower and upper
bounds of \Theta((log n) / k) if all valuations have the same maximum. We
expect our upper bound technique to be of broader interest; for example, it can
significantly improve the result of Akhlaghpour et al. [1]. We also initiate
the study of revenue maximization given allocative externalities (i.e.
influences) between buyers with combinatorial valuations. We provide a rather
general model of positive influence of others' ownership of items on a buyer's
valuation. For affine, submodular externalities and valuations with hereditary
maximizers we present an influence-and-exploit (Hartline et al. [13]) marketing
strategy based on our algorithm for private valuations. This strategy preserves
our approximation factor, despite an affine increase (due to externalities) in
the optimum revenue.Comment: 18 pages, 1 figur
Degree Distribution of Competition-Induced Preferential Attachment Graphs
We introduce a family of one-dimensional geometric growth models, constructed
iteratively by locally optimizing the tradeoffs between two competing metrics,
and show that this family is equivalent to a family of preferential attachment
random graph models with upper cutoffs. This is the first explanation of how
preferential attachment can arise from a more basic underlying mechanism of
local competition. We rigorously determine the degree distribution for the
family of random graph models, showing that it obeys a power law up to a finite
threshold and decays exponentially above this threshold.
We also rigorously analyze a generalized version of our graph process, with
two natural parameters, one corresponding to the cutoff and the other a
``fertility'' parameter. We prove that the general model has a power-law degree
distribution up to a cutoff, and establish monotonicity of the power as a
function of the two parameters. Limiting cases of the general model include the
standard preferential attachment model without cutoff and the uniform
attachment model.Comment: 24 pages, one figure. To appear in the journal: Combinatorics,
Probability and Computing. Note, this is a long version, with complete
proofs, of the paper "Competition-Induced Preferential Attachment"
(cond-mat/0402268
Maximum Edge-Disjoint Paths in -sums of Graphs
We consider the approximability of the maximum edge-disjoint paths problem
(MEDP) in undirected graphs, and in particular, the integrality gap of the
natural multicommodity flow based relaxation for it. The integrality gap is
known to be even for planar graphs due to a simple
topological obstruction and a major focus, following earlier work, has been
understanding the gap if some constant congestion is allowed.
In this context, it is natural to ask for which classes of graphs does a
constant-factor constant-congestion property hold. It is easy to deduce that
for given constant bounds on the approximation and congestion, the class of
"nice" graphs is nor-closed. Is the converse true? Does every proper
minor-closed family of graphs exhibit a constant factor, constant congestion
bound relative to the LP relaxation? We conjecture that the answer is yes.
One stumbling block has been that such bounds were not known for bounded
treewidth graphs (or even treewidth 3). In this paper we give a polytime
algorithm which takes a fractional routing solution in a graph of bounded
treewidth and is able to integrally route a constant fraction of the LP
solution's value. Note that we do not incur any edge congestion. Previously
this was not known even for series parallel graphs which have treewidth 2. The
algorithm is based on a more general argument that applies to -sums of
graphs in some graph family, as long as the graph family has a constant factor,
constant congestion bound. We then use this to show that such bounds hold for
the class of -sums of bounded genus graphs
Log-Networks
We introduce a growing network model in which a new node attaches to a
randomly-selected node, as well as to all ancestors of the target node. This
mechanism produces a sparse, ultra-small network where the average node degree
grows logarithmically with network size while the network diameter equals 2. We
determine basic geometrical network properties, such as the size dependence of
the number of links and the in- and out-degree distributions. We also compare
our predictions with real networks where the node degree also grows slowly with
time -- the Internet and the citation network of all Physical Review papers.Comment: 7 pages, 6 figures, 2-column revtex4 format. Version 2: minor changes
in response to referee comments and to another proofreading; final version
for PR
LP-based Covering Games with Low Price of Anarchy
We present a new class of vertex cover and set cover games. The price of
anarchy bounds match the best known constant factor approximation guarantees
for the centralized optimization problems for linear and also for submodular
costs -- in contrast to all previously studied covering games, where the price
of anarchy cannot be bounded by a constant (e.g. [6, 7, 11, 5, 2]). In
particular, we describe a vertex cover game with a price of anarchy of 2. The
rules of the games capture the structure of the linear programming relaxations
of the underlying optimization problems, and our bounds are established by
analyzing these relaxations. Furthermore, for linear costs we exhibit linear
time best response dynamics that converge to these almost optimal Nash
equilibria. These dynamics mimic the classical greedy approximation algorithm
of Bar-Yehuda and Even [3]
Less is more? Detecting lies in veiled witnesses
Judges in the United States, the United Kingdom, and Canada have ruled that witnesses may not wear the niqab-a type of face veil-when testifying, in part because they believed that it was necessary to see a person's face to detect deception (Muhammad v. Enterprise Rent-A-Car, 2006; R. v. N. S., 2010; The Queen v. D(R), 2013). In two studies, we used conventional research methods and safeguards to empirically examine the assumption that niqabs interfere with lie detection. Female witnesses were randomly assigned to lie or tell the truth while remaining unveiled or while wearing a hijab (i.e., a head veil) or a niqab (i.e., a face veil). In Study 1, laypersons in Canada (N = 232) were more accurate at detecting deception in witnesses who wore niqabs or hijabs than in those who did not wear veils. Concealing portions of witnesses' faces led laypersons to change their decision-making strategies without eliciting negative biases. Lie detection results were partially replicated in Study 2, with laypersons in Canada, the United Kingdom, and the Netherlands (N = 291): observers' performance was better when witnesses wore either niqabs or hijabs than when witnesses did not wear veils. These findings suggest that, contrary to judicial opinion, niqabs do not interfere with-and may, in fact, improve-the ability to detect deception
Degree distributions of growing networks
The in-degree and out-degree distributions of a growing network model are determined. The in-degree is the number of incoming links to a given node (and vice versa for out-degree. The network is built by (i) creation of new nodes which each immediately attach to a pre-existing node, and (ii) creation of new links between pre-existing nodes. This process naturally generates correlated in- and out-degree distributions. When the node and link creation rates are linear functions of node degree, these distributions exhibit distinct power-law forms. By tuning the parameters in these rates to reasonable values, exponents which agree with those of the web graph are obtained
- …