Abstract. We revisit a classical load balancing problem in the modern context of decentralized systems and self-interested clients. In particular, there is a set of clients, each of whom must choose a server from a permissible set. Each client has a unit-length job and selfishly wants to minimize its own latency (job completion time). A server's latency is inversely proportional to its speed, but it grows linearly with (or, more generally, as the pth power of) the number of clients matched to it. This interaction is naturally modeled as an atomic congestion game, which we call selfish load balancing. We analyze the Nash equilibria of this game and prove nearly tight bounds on the price of anarchy (worst-case ratio between a Nash solution and the social optimum). In particular, for linear latency functions, we show that if the server speeds are relatively bounded and the number of clients is large compared with the number of servers, then every Nash assignment approaches social optimum. Without any assumptions on the number of clients, servers, and server speeds, the price of anarchy is at most 2.5. If all servers have the same speed, then the price of anarchy further improves to 1 + 2/ √ 3 ≈ 2.15. We also exhibit a lower bound of 2.01. Our proof techniques can also be adapted for the coordinated load balancing problem under L 2 norm, where it slightly improves the best previously known upper bound on the competitive ratio of a simple greedy scheme.

The process of record linkage seeks to integrate instances that correspond to the same entity. Record linkage has traditionally been performed through the comparison of identifying field values (e.g., Surname), however, when databases are maintained by disparate organizations, the disclosure of such information can breach the privacy of the corresponding individuals. Various private record linkage (PRL) methods have been developed to obscure such identifiers, but they vary widely in their ability to balance competing goals of accuracy, efficiency and security. The tokenization and hashing of field values into Bloom filters (BF) enables greater linkage accuracy and efficiency than other PRL methods, but the encodings may be compromised through frequency-based cryptanalysis. Our objective is to adapt a BF encoding technique to mitigate such attacks with minimal sacrifices in accuracy and efficiency. To accomplish these goals, we introduce a statistically-informed method to generate BF encodings that integrate bits from multiple fields, the frequencies of which are provably associated with a minimum number of fields. Our method enables a user-specified tradeoff between security and accuracy. We compare our encoding method with other techniques using a public dataset of voter registration records and demonstrate that the increases in security come with only minor losses to accuracy.

We present a multi-dimensional generalization of the Szemerédi-Trotter Theorem, and give a sharp bound on the number of incidences of points and not-too-degenerate hyperplanes in three-or higher-dimensional Euclidean spaces. We call a hyperplane not-too-degenerate if at most a constant portion of its incident points lie in a lower dimensional affine subspace.

It is shown that n points and e lines in the complex Euclidean plane C 2 determine O(n 2/3 e 2/3 + n + e) point-line incidences. This bound is the best possible, and it generalizes the celebrated theorem by Szemerédi and Trotter about point-line incidences in the real Euclidean plane R 2 .

We obtain new lower and upper bounds for the maximum multiplicity of some weighted and, respectively, nonweighted common geometric graphs drawn on n points in the plane in general position (with no three points collinear): perfect matchings, spanning trees, spanning cycles (tours), and triangulations. (i) We present a new lower bound construction for the maximum number of triangulations a set of n points in general position can have. In particular, we show that a generalized double chain formed by two almost convex chains admits Ω(8.65 n ) different triangulations. This improves the bound Ω(8.48 n ) achieved by the previous best construction, the double zig-zag chain studied by Aichholzer et al. (ii) We obtain a new lower bound of Ω(12.00 n ) for the number of noncrossing spanning trees of the double chain composed of two convex chains. The previous bound, Ω(10.42 n ), stood unchanged for more than 10 years. (iii) Using a recent upper bound of 30 n for the number of triangulations, due to Sharir and Sheffer, we show that n points in the plane in general position admit at most O(68.62 n ) noncrossing spanning cycles. (iv) We derive lower bounds for the number of maximum and minimum weighted geometric graphs (matchings, spanning trees, and tours). We show that the number of shortest tours can be exponential in n for points in general position. These tours are automatically noncrossing. Likewise, we show that the number of longest noncrossing tours can be exponential in n. It was known that the number of shortest noncrossing perfect matchings can be exponential in n, and here we show that the number of longest noncrossing perfect matchings can be also exponential in n. It was known that the number of longest noncrossing spanning trees of a point set can be exponentially large, and here we show that this can be also realized with points in convex position. For points in convex position we re-derive tight bounds for the number of longest and shortest tours with some simpler arguments. We also give a combinatorial characterization of longest tours, which yields an O(n log n) time algorithm for computing them.

We revisit a classical load balancing problem in the modern context of decentralized systems and self-interested clients. In particular, there is a set of clients, each of whom must choose a server from a permissible set. Each client selfishly wants to minimize its own latency (job completion time). A server's latency is inversely proportional to its speed, but it grows linearly with (or, more generally, as the pth power of) the number of clients matched to it. This interaction is naturally modeled as an atomic congestion game, which we call selfish load balancing. We analyze the Nash equilibria of this game and prove nearly tight bounds on the price of anarchy (worst-case ratio between a Nash solution and the social optimum). In particular, for linear latency functions, we show that if the server speeds are relatively bounded and the number of clients is large compared to the number of servers, then every Nash assignment approaches social optimum. Without any assumptions on the number of clients, servers, and server speeds, the price of anarchy is at most 2.5. If all servers have the same speed, then the price of anarchy further improves to 1 + 2/ √ 3 ≈ 2.15. We also exhibit a lower bound of 2.01. Our proof techniques can also be adapted for the coordinated load balancing problem under L2 norm, where it slightly improves the best previously known upper bound on the competitive ratio of a simple greedy scheme.

Our study findings support the association between intra-amniotic infections and preterm delivery.

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