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We study the risks of validator reuse across multiple services in a restaking protocol. We characterize the robust security of a restaking network as a function of the buffer between the costs and profits from attacks. For example, our results imply that if attack costs always exceed attack profits by 10%, then a sudden loss of .1% of the overall stake (e.g., due to a software error) cannot result in the ultimate loss of more than 1.1% of the overall stake. We also provide local analogs of these overcollateralization conditions and robust security guarantees that apply specifically for a target service or coalition of services. All of our bounds on worst-case stake loss are the best possible. Finally, we bound the maximum-possible length of a cascade of attacks. Our results suggest measures of robustness that could be exposed to the participants in a restaking protocol. We also suggest polynomial-time computable sufficient conditions that can proxy for these measures. 

We study the stochastic vertex cover problem. In this problem, G = (V, E) is an arbitrary known graph, and G⋆ is an unknown random subgraph of G where each edge e is realized independently with probability p. Edges of G⋆ can only be verified using edge queries. The goal in this problem is to find a minimum vertex cover of G⋆ using a small number of queries. Our main result is designing an algorithm that returns a vertex cover of G⋆ with size at most (3/2+є) times the expected size of the minimum vertex cover, using only O(n/є p) non-adaptive queries. This improves over the best-known 2-approximation algorithm by Behnezhad, Blum and Derakhshan [SODA’22] who also show that Ω(n/p) queries are necessary to achieve any constant approximation. Our guarantees also extend to instances where edge realizations are not fully independent. We complement this upperbound with a tight 3/2-approximation lower bound for stochastic graphs whose edges realizations demonstrate mild correlations. 

Kidney exchanges allow patients with end-stage renal disease to find a lifesaving living donor by way of an organized market. However, not all patients are equally easy to match, nor are all donor organs of equal quality---some patients are matched within weeks, while others may wait for years with no match offers at all. We propose the first decision-support tool for kidney exchange that takes as input the biological features of a patient-donor pair, and returns (i) the probability of being matched prior to expiry, and (conditioned on a match outcome), (ii) the waiting time for and (iii) the organ quality of the matched transplant. This information may be used to inform medical and insurance decisions. We predict all quantities (i, ii, iii) exclusively from match records that are readily available in any kidney exchange using a quantile random forest approach. To evaluate our approach, we developed two state-of-the-art realistic simulators based on data from the United Network for Organ Sharing that sample from the training and test distribution for these learning tasks---in our application these distributions are distinct. We analyze distributional shift through a theoretical lens, and show that the two distributions converge as the kidney exchange nears steady-state. We then show that our approach produces clinically-promising estimates using simulated data. Finally, we show how our approach, in conjunction with tools from the model explainability literature, can be used to calibrate and detect bias in matching policies.