72 research outputs found
On Profit-Maximizing Pricing for the Highway and Tollbooth Problems
In the \emph{tollbooth problem}, we are given a tree \bT=(V,E) with
edges, and a set of customers, each of whom is interested in purchasing a
path on the tree. Each customer has a fixed budget, and the objective is to
price the edges of \bT such that the total revenue made by selling the paths
to the customers that can afford them is maximized. An important special case
of this problem, known as the \emph{highway problem}, is when \bT is
restricted to be a line.
For the tollbooth problem, we present a randomized -approximation,
improving on the current best -approximation. We also study a
special case of the tollbooth problem, when all the paths that customers are
interested in purchasing go towards a fixed root of \bT. In this case, we
present an algorithm that returns a -approximation, for any
, and runs in quasi-polynomial time. On the other hand, we rule
out the existence of an FPTAS by showing that even for the line case, the
problem is strongly NP-hard. Finally, we show that in the \emph{coupon model},
when we allow some items to be priced below zero to improve the overall profit,
the problem becomes even APX-hard
Improved Hardness of Approximation for Stackelberg Shortest-Path Pricing
We consider the Stackelberg shortest-path pricing problem, which is defined as follows. Given a graph G with fixed-cost and pricable edges and two distinct vertices s and t, we may assign prices to the pricable edges. Based on the predefined fixed costs and our prices, a customer purchases a cheapest s-t-path in G and we receive payment equal to the sum of prices of pricable edges belonging to the path. Our goal is to find prices maximizing the payment received from the customer. While Stackelberg shortest-path pricing was known to be APX-hard before, we provide the first explicit approximation threshold and prove hardness of approximation within 2−o(1). We also argue that the nicely structured type of instance resulting from our reduction captures most of the challenges we face in dealing with the problem in general and, in particular, we show that the gap between the revenue of an optimal pricing and the only known general upper bound can still be logarithmically large
Approximation Algorithms for the Max-Buying Problem with Limited Supply
We consider the Max-Buying Problem with Limited Supply, in which there are
items, with copies of each item , and bidders such that every
bidder has valuation for item . The goal is to find a pricing
and an allocation of items to bidders that maximizes the profit, where
every item is allocated to at most bidders, every bidder receives at most
one item and if a bidder receives item then . Briest
and Krysta presented a 2-approximation for this problem and Aggarwal et al.
presented a 4-approximation for the Price Ladder variant where the pricing must
be non-increasing (that is, ). We present an
-approximation for the Max-Buying Problem with Limited Supply and, for
every , a -approximation for the Price Ladder
variant
Optimal Pricing Is Hard
We show that computing the revenue-optimal deterministic auction in unit-demand single-buyer Bayesian settings, i.e. the optimal item-pricing, is computationally hard even in single-item settings where the buyer’s value distribution is a sum of independently distributed attributes, or multi-item settings where the buyer’s values for the items are independent. We also show that it is intractable to optimally price the grand bundle of multiple items for an additive bidder whose values for the items are independent. These difficulties stem from implicit definitions of a value distribution. We provide three instances of how different properties of implicit distributions can lead to intractability: the first is a #P-hardness proof, while the remaining two are reductions from the SQRT-SUM problem of Garey, Graham, and Johnson [14]. While simple pricing schemes can oftentimes approximate the best scheme in revenue, they can have drastically different underlying structure. We argue therefore that either the specification of the input distribution must be highly restricted in format, or it is necessary for the goal to be mere approximation to the optimal scheme’s revenue instead of computing properties of the scheme itself.Microsoft Research (Fellowship)Alfred P. Sloan Foundation (Fellowship)National Science Foundation (U.S.) (CAREER Award CCF-0953960)National Science Foundation (U.S.) (Award CCF-1101491)Hertz Foundation (Daniel Stroock Fellowship
Assortment optimisation under a general discrete choice model: A tight analysis of revenue-ordered assortments
The assortment problem in revenue management is the problem of deciding which
subset of products to offer to consumers in order to maximise revenue. A simple
and natural strategy is to select the best assortment out of all those that are
constructed by fixing a threshold revenue and then choosing all products
with revenue at least . This is known as the revenue-ordered assortments
strategy. In this paper we study the approximation guarantees provided by
revenue-ordered assortments when customers are rational in the following sense:
the probability of selecting a specific product from the set being offered
cannot increase if the set is enlarged. This rationality assumption, known as
regularity, is satisfied by almost all discrete choice models considered in the
revenue management and choice theory literature, and in particular by random
utility models. The bounds we obtain are tight and improve on recent results in
that direction, such as for the Mixed Multinomial Logit model by
Rusmevichientong et al. (2014). An appealing feature of our analysis is its
simplicity, as it relies only on the regularity condition.
We also draw a connection between assortment optimisation and two pricing
problems called unit demand envy-free pricing and Stackelberg minimum spanning
tree: These problems can be restated as assortment problems under discrete
choice models satisfying the regularity condition, and moreover revenue-ordered
assortments correspond then to the well-studied uniform pricing heuristic. When
specialised to that setting, the general bounds we establish for
revenue-ordered assortments match and unify the best known results on uniform
pricing.Comment: Minor changes following referees' comment
Combinatorial Auctions without Money
Algorithmic Mechanism Design attempts to marry computation and incentives, mainly by leveraging monetary transfers between designer and selfish agents involved. This is principally because in absence of money, very little can be done to enforce truthfulness. However, in certain applications, money is unavailable, morally unacceptable or might simply be at odds with the objective of the mechanism. For example, in Combinatorial Auctions (CAs), the paradigmatic problem of the area, we aim at solutions of maximum social welfare, but still charge the society to ensure truthfulness. We focus on the design of incentive-compatible CAs without money in the general setting of k-minded bidders. We trade monetary transfers with the observation that the mechanism can detect certain lies of the bidders: i.e., we study truthful CAs with verification and without money. In this setting, we characterize the class of truthful mechanisms and give a host of upper and lower bounds on the approximation ratio obtained by either deterministic or randomized truthful mechanisms. Our results provide an almost complete picture of truthfully approximating CAs in this general setting with multi-dimensional bidders
Improved Approximation Algorithms for Box Contact Representations ⋆
Abstract. We study the following geometric representation problem: Given a graph whose vertices correspond to axis-aligned rectangles with fixed dimensions, arrange the rectangles without overlaps in the plane such that two rectangles touch if the graph contains an edge between them. This problem is called CONTACT REPRESENTATION OF WORD NETWORKS (CROWN) since it formalizes the geometric problem behind drawing word clouds in which semantically related words are close to each other. CROWN is known to be NP-hard, and there are approximation algorithms for certain graph classes for the optimization version, MAX-CROWN, in which realizing each desired adjacency yields a certain profit. We present the first O(1)-approximation algorithm for the general case, when the input is a complete weighted graph, and for the bipartite case. Since the subgraph of realized adjacencies is necessarily planar, we also consider several planar graph classes (namely stars, trees, outerplanar, and planar graphs), improving upon the known results. For some graph classes, we also describe improvements in the unweighted case, where each adjacency yields the same profit. Finally, we show that the problem is APX-hard on bipartite graphs of bounded maximum degree.
Does the proteasome inhibitor bortezomib sensitize to DNA-damaging therapy in gastroenteropancreatic neuroendocrine neoplasms? - A preclinical assessment in vitro and in vivo
BACKGROUND: Well-differentiated gastroenteropancreatic neuroendocrine neoplasms are rare tumors with a slow proliferation. They are virtually resistant to many DNA-damaging therapeutic approaches, such as chemo- and external beam therapy, which might be overcome by DNA damage inhibition induced by proteasome inhibitors such as bortezomib. METHODS AND RESULTS: In this study, we assessed several combined treatment modalities in vitro and in vivo. By cell-based functional analyses, in a 3D in ovo and an orthotopic mouse model, we demonstrated sensitizing effects of bortezomib combined with cisplatin, radiation and peptide receptor radionuclide therapy (PRRT). By gene expression profiling and western blot, we explored the underlying mechanisms, which resulted in an impaired DNA damage repair. Therapy-induced DNA damage triggered extrinsic proapoptotic signaling as well as the induction of cell cycle arrest, leading to a decreased vital tumor volume and altered tissue composition shown by magnetic resonance imaging and F-18-FDG-PET in vivo, however with no significant additional benefit related to PRRT alone. CONCLUSIONS: We demonstrated that bortezomib has short-term sensitizing effects when combined with DNA damaging therapy by interfering with DNA repair in vitro and in ovo. Nevertheless, due to high tumor heterogeneity after PRRT in long-term observations, we were not able to prove a therapeutic advantage of bortezomib-combined PRRT in an in vivo mouse model
Does the proteasome inhibitor bortezomib sensitize to DNA-damaging therapy in gastroenteropancreatic neuroendocrine neoplasms? – A preclinical assessment in vitro and in vivo
Background: Well-differentiated gastroenteropancreatic neuroendocrine neoplasms are rare tumors with a slow proliferation. They are virtually resistant to many DNA-damaging therapeutic approaches, such as chemo- and external beam therapy, which might be overcome by DNA damage inhibition induced by proteasome inhibitors suc
- …