TY - JOUR AB - We study multiple keyword sponsored search auctions with budgets. Each keyword has multiple ad slots with a click-through rate. The bidders have additive valuations, which are linear in the click-through rates, and budgets, which are restricting their overall payments. Additionally, the number of slots per keyword assigned to a bidder is bounded. We show the following results: (1) We give the first mechanism for multiple keywords, where click-through rates differ among slots. Our mechanism is incentive compatible in expectation, individually rational in expectation, and Pareto optimal. (2) We study the combinatorial setting, where each bidder is only interested in a subset of the keywords. We give an incentive compatible, individually rational, Pareto-optimal, and deterministic mechanism for identical click-through rates. (3) We give an impossibility result for incentive compatible, individually rational, Pareto-optimal, and deterministic mechanisms for bidders with diminishing marginal valuations. AU - Colini-Baldeschi, Riccardo AU - Leonardi, Stefano AU - Henzinger, Monika H AU - Starnberger, Martin ID - 11668 IS - 1 JF - ACM Transactions on Economics and Computation KW - Algorithms KW - Economics KW - Clinching ascending auction KW - auctions with budgets KW - Sponsored search auctions SN - 2167-8375 TI - On multiple keyword sponsored search auctions with budgets VL - 4 ER - TY - JOUR AB - We study individual rational, Pareto-optimal, and incentive compatible mechanisms for auctions with heterogeneous items and budget limits. We consider settings with multiunit demand and additive valuations. For single-dimensional valuations we prove a positive result for randomized mechanisms, and a negative result for deterministic mechanisms. While the positive result allows for private budgets, the negative result is for public budgets. For multidimensional valuations and public budgets we prove an impossibility result that applies to deterministic and randomized mechanisms. Taken together this shows the power of randomization in certain settings with heterogeneous items, but it also shows its limitations. AU - Dütting, Paul AU - Henzinger, Monika H AU - Starnberger, Martin ID - 11669 IS - 1 JF - ACM Transactions on Economics and Computation KW - Algorithmic game theory KW - auction theory KW - Clinching auction KW - Pareto optimality KW - Budget limits SN - 2167-8375 TI - Auctions for heterogeneous items and budget limits VL - 4 ER - TY - JOUR AB - Auctions are widely used on the Web. Applications range from sponsored search to platforms such as eBay. In these and in many other applications the auctions in use are single-/multi-item auctions with unit demand. The main drawback of standard mechanisms for this type of auctions, such as VCG and GSP, is the limited expressiveness that they offer to the bidders. The General Auction Mechanism (GAM) of Aggarwal et al. [2009] takes a first step toward addressing the problem of limited expressiveness by computing a bidder optimal, envy-free outcome for linear utility functions with identical slopes and a single discontinuity per bidder-item pair. We show that in many practical situations this does not suffice to adequately model the preferences of the bidders, and we overcome this problem by presenting the first mechanism for piecewise linear utility functions with nonidentical slopes and multiple discontinuities. Our mechanism runs in polynomial time. Like GAM it is incentive compatible for inputs that fulfill a certain nondegeneracy assumption, but our requirement is more general than the requirement of GAM. For discontinuous utility functions that are nondegenerate as well as for continuous utility functions the outcome of our mechanism is a competitive equilibrium. We also show how our mechanism can be used to compute approximately bidder optimal, envy-free outcomes for a general class of continuous utility functions via piecewise linear approximation. Finally, we prove hardness results for even more expressive settings. AU - Dütting, Paul AU - Henzinger, Monika H AU - Weber, Ingmar ID - 11670 IS - 1 JF - ACM Transactions on Economics and Computation KW - Computational Mathematics KW - Marketing KW - Economics and Econometrics KW - Statistics and Probability KW - Computer Science (miscellaneous) SN - 2167-8375 TI - An expressive mechanism for auctions on the web VL - 4 ER - TY - CONF AB - Combinatorial auctions (CA) are a well-studied area in algorithmic mechanism design. However, contrary to the standard model, empirical studies suggest that a bidder’s valuation often does not depend solely on the goods assigned to him. For instance, in adwords auctions an advertiser might not want his ads to be displayed next to his competitors’ ads. In this paper, we propose and analyze several natural graph-theoretic models that incorporate such negative externalities, in which bidders form a directed conflict graph with maximum out-degree Δ. We design algorithms and truthful mechanisms for social welfare maximization that attain approximation ratios depending on Δ. For CA, our results are twofold: (1) A lottery that eliminates conflicts by discarding bidders/items independent of the bids. It allows to apply any truthful 𝛼-approximation mechanism for conflict-free valuations and yields an 𝒪(𝛼Δ)-approximation mechanism. (2) For fractionally sub-additive valuations, we design a rounding algorithm via a novel combination of a semi-definite program and a linear program, resulting in a cone program; the approximation ratio is 𝒪((ΔloglogΔ)/logΔ). The ratios are almost optimal given existing hardness results. For adwords auctions, we present several algorithms for the most relevant scenario when the number of items is small. In particular, we design a truthful mechanism with approximation ratio 𝑜(Δ) when the number of items is only logarithmic in the number of bidders. AU - Cheung, Yun Kuen AU - Henzinger, Monika H AU - Hoefer, Martin AU - Starnberger, Martin ID - 11774 SN - 0302-9743 T2 - 11th International Conference on Web and Internet Economics TI - Combinatorial auctions with conflict-based externalities VL - 9470 ER - TY - CONF AB - Ad exchanges are an emerging platform for trading advertisement slots on the web with billions of dollars revenue per year. Every time a user visits a web page, the publisher of that web page can ask an ad exchange to auction off the ad slots on this page to determine which advertisements are shown at which price. Due to the high volume of traffic, ad networks typically act as mediators for individual advertisers at ad exchanges. If multiple advertisers in an ad network are interested in the ad slots of the same auction, the ad network might use a “local” auction to resell the obtained ad slots among its advertisers. In this work we want to deepen the theoretical understanding of these new markets by analyzing them from the viewpoint of combinatorial auctions. Prior work studied mostly single-item auctions, while we allow the advertisers to express richer preferences over multiple items. We develop a game-theoretic model for the entanglement of the central auction at the ad exchange with the local auctions at the ad networks. We consider the incentives of all three involved parties and suggest a three-party competitive equilibrium, an extension of the Walrasian equilibrium that ensures envy-freeness for all participants. We show the existence of a three-party competitive equilibrium and a polynomial-time algorithm to find one for gross-substitute bidder valuations. AU - Ben-Zwi, Oren AU - Henzinger, Monika H AU - Loitzenbauer, Veronika ID - 11773 SN - 0302-9743 T2 - 11th International Conference on Web and Internet Economics TI - Ad exchange: Envy-free auctions with mediators VL - 9470 ER - TY - CONF AB - Recently we presented the first algorithm for maintaining the set of nodes reachable from a source node in a directed graph that is modified by edge deletions with 𝑜(𝑚𝑛) total update time, where 𝑚 is the number of edges and 𝑛 is the number of nodes in the graph [Henzinger et al. STOC 2014]. The algorithm is a combination of several different algorithms, each for a different 𝑚 vs. 𝑛 trade-off. For the case of 𝑚=Θ(𝑛1.5) the running time is 𝑂(𝑛2.47), just barely below 𝑚𝑛=Θ(𝑛2.5). In this paper we simplify the previous algorithm using new algorithmic ideas and achieve an improved running time of 𝑂̃ (min(𝑚7/6𝑛2/3,𝑚3/4𝑛5/4+𝑜(1),𝑚2/3𝑛4/3+𝑜(1)+𝑚3/7𝑛12/7+𝑜(1))). This gives, e.g., 𝑂(𝑛2.36) for the notorious case 𝑚=Θ(𝑛1.5). We obtain the same upper bounds for the problem of maintaining the strongly connected components of a directed graph undergoing edge deletions. Our algorithms are correct with high probabililty against an oblivious adversary. AU - Henzinger, Monika H AU - Krinninger, Sebastian AU - Nanongkai, Danupon ID - 11785 SN - 0302-9743 T2 - 42nd International Colloquium on Automata, Languages and Programming TI - Improved algorithms for decremental single-source reachability on directed graphs VL - 9134 ER - TY - CONF AB - We present faster algorithms for computing the 2-edge and 2-vertex strongly connected components of a directed graph. While in undirected graphs the 2-edge and 2-vertex connected components can be found in linear time, in directed graphs with m edges and n vertices only rather simple O(m n)-time algorithms were known. We use a hierarchical sparsification technique to obtain algorithms that run in time 𝑂(𝑛2). For 2-edge strongly connected components our algorithm gives the first running time improvement in 20 years. Additionally we present an 𝑂(𝑚2/log𝑛)-time algorithm for 2-edge strongly connected components, and thus improve over the O(m n) running time also when 𝑚=𝑂(𝑛). Our approach extends to k-edge and k-vertex strongly connected components for any constant k with a running time of 𝑂(𝑛2log𝑛) for k-edge-connectivity and 𝑂(𝑛3) for k-vertex-connectivity. AU - Henzinger, Monika H AU - Krinninger, Sebastian AU - Loitzenbauer, Veronika ID - 11787 SN - 0302-9743 T2 - 2nd International Colloquium on Automata, Languages and Programming TI - Finding 2-edge and 2-vertex strongly connected components in quadratic time VL - 9134 ER - TY - CONF AB - Ad exchanges are becoming an increasingly popular way to sell advertisement slots on the internet. An ad exchange is basically a spot market for ad impressions. A publisher who has already signed contracts reserving advertisement impressions on his pages can choose between assigning a new ad impression for a new page view to a contracted advertiser or to sell it at an ad exchange. This leads to an online revenue maximization problem for the publisher. Given a new impression to sell decide whether (a) to assign it to a contracted advertiser and if so to which one or (b) to sell it at the ad exchange and if so at which reserve price. We make no assumptions about the distribution of the advertiser valuations that participate in the ad exchange and show that there exists a simple primal-dual based online algorithm, whose lower bound for the revenue converges to 𝑅𝐴𝐷𝑋+𝑅𝐴(1−1/𝑒), where 𝑅𝐴𝐷𝑋 is the revenue that the optimum algorithm achieves from the ad exchange and 𝑅𝐴 is the revenue that the optimum algorithm achieves from the contracted advertisers. AU - Dvořák, Wolfgang AU - Henzinger, Monika H ID - 11788 SN - 0302-9743 T2 - 12th International Workshop of Approximation and Online Algorithms TI - Online ad assignment with an ad exchange VL - 8952 ER - TY - CONF AB - In this paper, we develop a dynamic version of the primal-dual method for optimization problems, and apply it to obtain the following results. (1) For the dynamic set-cover problem, we maintain an 𝑂(𝑓2)-approximately optimal solution in 𝑂(𝑓⋅log(𝑚+𝑛)) amortized update time, where 𝑓 is the maximum “frequency” of an element, 𝑛 is the number of sets, and 𝑚 is the maximum number of elements in the universe at any point in time. (2) For the dynamic 𝑏-matching problem, we maintain an 𝑂(1)-approximately optimal solution in 𝑂(log3𝑛) amortized update time, where 𝑛 is the number of nodes in the graph. AU - Bhattacharya, Sayan AU - Henzinger, Monika H AU - Italiano, Giuseppe F. ID - 11786 SN - 0302-9743 T2 - 42nd International Colloquium on Automata, Languages and Programming TI - Design of dynamic algorithms via primal-dual method VL - 9134 ER - TY - JOUR AB - Phylogenetic diversity (PD) is a measure of biodiversity based on the evolutionary history of species. Here, we discuss several optimization problems related to the use of PD, and the more general measure split diversity (SD), in conservation prioritization. Depending on the conservation goal and the information available about species, one can construct optimization routines that incorporate various conservation constraints. We demonstrate how this information can be used to select sets of species for conservation action. Specifically, we discuss the use of species' geographic distributions, the choice of candidates under economic pressure, and the use of predator–prey interactions between the species in a community to define viability constraints. Despite such optimization problems falling into the area of NP hard problems, it is possible to solve them in a reasonable amount of time using integer programming. We apply integer linear programming to a variety of models for conservation prioritization that incorporate the SD measure. We exemplarily show the results for two data sets: the Cape region of South Africa and a Caribbean coral reef community. Finally, we provide user-friendly software at http://www.cibiv.at/software/pda. AU - Chernomor, Olga AU - Minh, Bui Quang AU - Forest, Félix AU - Klaere, Steffen AU - Ingram, Travis AU - Henzinger, Monika H AU - von Haeseler, Arndt ID - 11845 IS - 1 JF - Methods in Ecology and Evolution TI - Split diversity in constrained conservation prioritization using integer linear programming VL - 6 ER -