Polyvalent Parallelizations for Hierarchical Block Matching Motion Estimation

Block matching motion estimation algorithms are widely used in video coding schemes. In this paper,we design an efficient hierarchical block matching motion estimation (HBMME) algorithm on a hypercube multiprocessor. Unlike systolic array designs, this solution is not tied down to specific values of algorithm parameters and thus offers increased flexibility. Moreover, the hypercube network can efficiently handle the non regular data flow of the HBMME algorithm. Our techniques nearly eliminate the occurrence of “difficult” communication patterns, namely many-to-many personalized communication, by replacing them with simple shift operations. These operations have an efficient implementation on most of interconnection networks and thus our techniques can be adapted to other networks as well. With regard to the employed multiprocessor we make no specific assumption about the amount of local memory residing in each processor. Instead, we introduce a free parameter S and assume that each processor has O(S) local memory. By doing so, we handle all the cases of modern multiprocessors, that is fine-grained, medium-grained and coarse-grained multiprocessors and thus our design is quite general

Limitations of Deterministic Auction Design for Correlated Bidders

The seminal work of Myerson (Mathematics of OR ’81) characterizes incentive-compatible single-item auctions among bidders with independent valuations. In this setting, relatively simple deterministic auction mechanisms achieve revenue optimality. When bidders have correlated valuations, designing the revenue-optimal deterministic auction is a computationally demanding problem; indeed, Papadimitriou and Pierrakos (STOC ’11) proved that it is APX-hard, obtaining an explicit inapproximability factor of 1999/2000 = 99.95%. In the current paper, we strengthen this inapproximability factor to 63/64 ≈ 98.5%. Our proof is based on a gap-preserving reduction from the Max-NM 3SAT problem; a variant of the maximum satisfiability problem where each clause has exactly 3 literals and no clause contains both negated and unnegated literals. We furthermore show that the gap between the revenue of deterministic and randomized auctions can be as low as 13/14 ≈ 92.9%, improving an explicit gap of 947/948 ≈ 99.9% by Dobzinski, Fu, and Kleinberg (STOC ’11)

Tight approximation bounds for combinatorial frugal coverage algorithms

We consider the frugal coverage problem, an interesting variation of set cover defined as follows. Instances of the problem consist of a universe of elements and a collection of sets over these elements; the objective is to compute a subcollection of sets so that the number of elements it covers plus the number of sets not chosen is maximized. The problem was introduced and studied by Huang and Svitkina (Proceedings of the 29th IARCS annual conference on foundations of software technology and theoretical computer science (FSTTCS), pp. 227–238, 2009) due to its connections to the donation center location problem. We prove that the greedy algorithm has approximation ratio at least 0.782, improving a previous bound of 0.731 in Huang and Svitkina (Proceedings of the 29th IARCS annual conference on foundations of software technology and theoretical computer science (FSTTCS), pp. 227–238, 2009). We also present a further improvement that is obtained by adding a simple corrective phase at the end of the execution of the greedy algorithm. The approximation ratio achieved in this way is at least 0.806. Finally, we consider a packing based algorithm that uses semi-local optimization, and show that its approximation ratio is not less than 0.872. Our analysis is based on the use of linear programs which capture the behavior of the algorithms in worst-case examples. The obtained bounds are proved to be tight

On the price of stability of some simple graph-based hedonic games

We consider graph-based hedonic games such as simple symmetric fractional hedonic games and social distance games, where a group of utility maximizing players have hedonic preferences over the players’ set, and wish to be partitioned into clusters so that they are grouped together with players they prefer. The players are nodes in a connected graph and their preferences are defined so that shorter graph distance implies higher preference. We are interested in Nash equilibria of such games, where no player has an incentive to unilaterally deviate to another cluster, and we focus on the notion of the price of stability. We present new and improved bounds on the price of stability for several graph classes, as well as for a slightly modified utility function

Fractional path coloring on bounded degree trees

International audienceThis paper addresses the natural relaxation of the path coloring problem, in which one needs to color directed paths on a symmetric directed graph with a minimum number of colors, in such a way that paths using the same arc of the graph have different colors. This classic combinatorial problem finds applications in the minimization of the number of wavelengths in wavelength division multiplexing (wdm) all-optical networks

Revenue Guarantees in the Generalized Second Price Auction

Sponsored search auctions are the main source of revenue for search engines. In such an auction, a set of utility maximizing advertisers competes for a set of ad slots. The assignment of advertisers to slots depends on the bids they submit; these bids may be different than the true valuations of the advertisers for the slots. Variants of the celebrated VCG auction mechanism guarantee that advertisers act truthfully and, under some assumptions, lead to revenue or social welfare maximization. Still, the sponsored search industry mostly uses generalized second price (GSP) auctions; these auctions are known to be nontruthful and suboptimal in terms of social welfare and revenue. In an attempt to explain this tradition, we study a Bayesian setting wherein the valuations of advertisers are drawn independently from a common regular probability distribution. In this setting, it is well known from the work of Myerson [1981] that the optimal revenue is obtained by the VCG mechanism with a particular reserve price that depends on the probability distribution. We show that, by appropriately setting the reserve price, the revenue over any Bayes-Nash equilibrium of the game induced by the GSP auction is at most a small constant factor away from the optimal revenue, improving previous results of Lucier et al. [2012]. Our analysis is based on the Bayes-Nash equilibrium conditions and the improved results are obtained by bounding the utility of each player at equilibrium using infinitely many deviating bids and also by developing novel prophet-like inequalities

On the Approximability of Dodgson and Young Elections

The voting rules proposed by Dodgson and Young are both designed to nd the alternative closest to being a Condorcet winner, according to two di erent notions of proximity; the score of a given alternative is known to be hard to compute under either rule. In this paper, we put forward two algorithms for ap- proximating the Dodgson score: an LP-based randomized rounding algorithm and a deterministic greedy algorithm, both of which yield an O(logm) approximation ratio, where m is the number of alternatives; we observe that this result is asymptotically optimal, and further prove that our greedy algorithm is optimal up to a factor of 2, unless problems in NP have quasi-polynomial time algorithms. Although the greedy algorithm is computationally superior, we argue that the randomized rounding algorithm has an advantage from a social choice point of view. Further, we demonstrate that computing any reasonable approximation of the ranking produced by Dodgson\u27s rule is NP-hard. This result provides a complexity-theoretic explanation of sharp discrepancies that have been observed in the Social Choice Theory literature when comparing Dodgson elections with simpler voting rules. Finally, we show that the problem of calculating the Young score is NP-hard to approximate by any factor. This leads to an inapproximability result for the Young ranking

Approximate Constrained Bipartite Edge Coloring

International audienceWe study the following Constrained Bipartite Edge Coloring (CBEC) problem: We are given a bipartite graph G(U,V,E) of maximum degree l with n vertices, in which some of the edges have been legally colored with c colors. We wish to complete the coloring of the edges of G minimizing the total number of colors used. The problem has been proved to be NP-hard event for bipartite graphs of maximum degree three

Interrelated modulation of endothelial function in Behcet's disease by clinical activity and corticosteroid treatment

Corticosteroids are commonly used in empirical treatment of Behçet's disease (BD), a systemic inflammatory condition associated with reversible endothelial dysfunction. In the present study we aimed to dissect the effects of clinical disease activity and chronic or short-term corticosteroid treatment on endothelial function in patients with BD. In a case-control, cross-sectional study, we assessed endothelial function by endothelium dependent flow mediated dilatation (FMD) at the brachial artery of 87 patients, who either were or were not receiving chronic corticosteroid treatment, and exhibiting variable clinical disease activity. Healthy individuals matched for age and sex served as controls. Endothelial function was also assessed in a prospective study of 11 patients before and after 7 days of treatment with prednisolone given at disease relapse (20 mg/day). In the cross-sectional component of the study, FMD was lower in patients than in control individuals (mean ± standard error: 4.1 ± 0.4% versus 5.7 ± 0.2%, P = 0.003), whereas there was a significant interaction between the effects of corticosteroids and disease activity on endothelial function (P = 0.014, two-factor analysis of variance). Among patients with inactive BD, those who were not treated with corticosteroids (n = 33) had FMD comparable to that in healthy control individuals, whereas those treated with corticosteroids (n = 15) had impaired endothelial function (P = 0.023 versus the respective control subgroup). In contrast, among patients with active BD, those who were not treated with corticosteroids (n = 20) had lower FMD than control individuals (P = 0.007), but in those who were receiving corticosteroids (n = 19) the FMD values were comparable to those in control individuals. Moreover, FMD was significantly improved after 7 days of prednisolone administration (3.7 ± 0.9% versus 7.6 ± 1.4%, P = 0.027). Taken together, these results imply that although corticosteroid treatment may impair endothelial function per se during the remission phase of the inflammatory process, it restores endothelial dysfunction during active BD by counteracting the harmful effects of relapsing inflammation