Optimally Efficient Multi-party Fair Exchange and Fair Secure Multi-party Computation

Multi-party fair exchange (MFE) and fair secure multi-party computation (fair SMPC) are under-studied fields of research, with practical importance. In particular, we consider MFE scenarios where at the end of the protocol, either every participant receives every other participant’s item, or no participant receives anything. We analyze the case where a trusted third party (TTP) is optimistically available, although we emphasize that the trust put on the TTP is only regarding the fairness , and our protocols preserve the privacy of the exchanged items against the TTP. In the fair SMPC case, we prove that a malicious TTP can only harm fairness, but not security . We construct an asymptotically optimal multi-party fair exchange protocol that requires a constant number of rounds (in comparison to linear) and O(n 2 ) messages (in comparison to cubic), where n is the number of participating parties. In our protocol, we enable the parties to efficiently exchange any item that can be efficiently put into a verifiable encryption (e.g., signatures on a contract). We show how to apply this protocol on top of any SMPC protocol to achieve fairness with very little overhead (independent of the circuit size). We then generalize our protocol to efficiently handle any exchange topology (participants exchange items with arbitrary other participants). Our protocol guarantees fairness in its strongest sense: even if all n-1 other participants are malicious and colluding with each other, the fairness is still guaranteed.

Asymptotically Optimal Sequential Design for Rank Aggregation

A sequential design problem for rank aggregation is commonly encountered in psychology, politics, marketing, sports, etc. In this problem, a decision maker is responsible for ranking K items by sequentially collecting noisy pairwise comparisons from judges. The decision maker needs to choose a pair of items for comparison in each step, decide when to stop data collection, and make a final decision after stopping based on a sequential flow of information. Because of the complex ranking structure, existing sequential analysis methods are not suitable. In this paper, we formulate the problem under a Bayesian decision framework and propose sequential procedures that are asymptotically optimal. These procedures achieve asymptotic optimality by seeking a balance between exploration (i.e., finding the most indistinguishable pair of items) and exploitation (i.e., comparing the most indistinguishable pair based on the current information). New analytical tools are developed for proving the asymptotic results, combining advanced change of measure techniques for handling the level crossing of likelihood ratios and classic large deviation results for martingales, which are of separate theoretical interest in solving complex sequential design problems. A mirror-descent algorithm is developed for the computation of the proposed sequential procedures.

A simpler linear-time algorithm for the common refinement of rooted phylogenetic trees on a common leaf set

Background The supertree problem, i.e., the task of finding a common refinement of a set of rooted trees is an important topic in mathematical phylogenetics. The special case of a common leaf set L is known to be solvable in linear time. Existing approaches refine one input tree using information of the others and then test whether the results are isomorphic. Results An O(k|L|) algorithm, , for constructing the common refinement T of k input trees with a common leaf set L is proposed that explicitly computes the parent function of T in a bottom-up approach. Conclusion is simpler to implement than other asymptotically optimal algorithms for the problem and outperforms the alternatives in empirical comparisons. Availability An implementation of in Python is freely available at https://github.com/david-schaller/tralda.

Efficient Covering of Thin Convex Domains Using Congruent Discs

We present efficient strategies for covering classes of thin domains in the plane using unit discs. We start with efficient covering of narrow domains using a single row of covering discs. We then move to efficient covering of general rectangles by discs centered at the lattice points of an irregular hexagonal lattice. This optimization uses a lattice that leads to a covering using a small number of discs. We compare the bounds on the covering using the presented strategies to the bounds obtained from the standard honeycomb covering, which is asymptotically optimal for fat domains, and show the improvement for thin domains.

Sequential metric dimension for random graphs

In the localization game on a graph, the goal is to find a fixed but unknown target node $v^\star$ with the least number of distance queries possible. In the jth step of the game, the player queries a single node $v_j$ and receives, as an answer to their query, the distance between the nodes $v_j$ and $v^\star$ . The sequential metric dimension (SMD) is the minimal number of queries that the player needs to guess the target with absolute certainty, no matter where the target is.The term SMD originates from the related notion of metric dimension (MD), which can be defined the same way as the SMD except that the player’s queries are non-adaptive. In this work we extend the results of Bollobás, Mitsche, and Prałat [4] on the MD of Erdős–Rényi graphs to the SMD. We find that, in connected Erdős–Rényi graphs, the MD and the SMD are a constant factor apart. For the lower bound we present a clean analysis by combining tools developed for the MD and a novel coupling argument. For the upper bound we show that a strategy that greedily minimizes the number of candidate targets in each step uses asymptotically optimal queries in Erdős–Rényi graphs. Connections with source localization, binary search on graphs, and the birthday problem are discussed.

Tight and Scalable Side-Channel Attack Evaluations through Asymptotically Optimal Massey-like Inequalities on Guessing Entropy

The bounds presented at CHES 2017 based on Massey’s guessing entropy represent the most scalable side-channel security evaluation method to date. In this paper, we present an improvement of this method, by determining the asymptotically optimal Massey-like inequality and then further refining it for finite support distributions. The impact of these results is highlighted for side-channel attack evaluations, demonstrating the improvements over the CHES 2017 bounds.

A Fluid-Diffusion-Hybrid Limiting Approximation for Priority Systems with Fast and Slow Customers

The paper “Fluid-Diffusion-Hybrid (FDH) Approximation” proposes a new heavy-traffic asymptotic regime for a two-class priority system in which the high-priority customers require substantially larger service times than the low-priority customers. In the FDH limit, the high-priority queue is a diffusion, whereas the low-priority queue operates as a (random) fluid limit, whose dynamics are driven by the former diffusion. A characterizing property of our limit process is that, unlike other asymptotic regimes, a non-negligible proportion of the customers from both classes must wait for service. This property allows us to study the costs and benefits of de-pooling, and prove that a two-pool system is often the asymptotically optimal design of the system.

Approximate Minimum Selection with Unreliable Comparisons

We consider the approximate minimum selection problem in presence of independent random comparison faults. This problem asks to select one of the smallest k elements in a linearly-ordered collection of n elements by only performing unreliable pairwise comparisons: whenever two elements are compared, there is a small probability that the wrong comparison outcome is observed. We design a randomized algorithm that solves this problem with a success probability of at least $$1-q$$ 1 - q for $$q \in (0, \frac{n-k}{n})$$ q ∈ ( 0 , n - k n ) and any $$k \in [1, n-1]$$ k ∈ [ 1 , n - 1 ] using $$O\big ( \frac{n}{k} \big \lceil \log \frac{1}{q} \big \rceil \big )$$ O ( n k ⌈ log 1 q ⌉ ) comparisons in expectation (if $$k \ge n$$ k ≥ n or $$q \ge \frac{n-k}{n}$$ q ≥ n - k n the problem becomes trivial). Then, we prove that the expected number of comparisons needed by any algorithm that succeeds with probability at least $$1-q$$ 1 - q must be $${\varOmega }(\frac{n}{k}\log \frac{1}{q})$$ Ω ( n k log 1 q ) whenever q is bounded away from $$\frac{n-k}{n}$$ n - k n , thus implying that the expected number of comparisons performed by our algorithm is asymptotically optimal in this range. Moreover, we show that the approximate minimum selection problem can be solved using $$O( (\frac{n}{k} + \log \log \frac{1}{q}) \log \frac{1}{q})$$ O ( ( n k + log log 1 q ) log 1 q ) comparisons in the worst case, which is optimal when q is bounded away from $$\frac{n-k}{n}$$ n - k n and $$k = O\big ( \frac{n}{\log \log \frac{1}{q}}\big )$$ k = O ( n log log 1 q ) .

Asymptotically Optimal Lagrangian Policies for Multi-Warehouse, Multi-Store Systems with Lost Sales

Simple Algorithms for Complex Multiwarehouse, Multistore Inventory Control Problems Retailers (both brick-and-mortar and e-commerce) have always faced the problem of allocating inventories in their warehouses (or central distribution centers) to the stores (or smaller local warehouses) in order to minimize total costs. The problem is particularly challenging when the network structure is large and complex, the selling season is long, and the replenishment is frequent. For example, giant retail chains such as Macy’s typically have many warehouses and hundreds of stores across the United States, and online retailers such as Amazon have many distribution centers and over one hundred fulfillment centers. The authors develop algorithms to solve this multiwarehouse, multistore (MWMS) inventory control problem. Their algorithms are computationally efficient and asymptotically optimal as the problem becomes large and complex. This feature is very appealing to today’s fast-moving retail industry with rapidly expanding business scale.

Control of Fork-Join Processing Networks with Multiple Job Types and Parallel Shared Resources

A fork-join processing network is a queueing network in which tasks associated with a job can be processed simultaneously. Fork-join processing networks are prevalent in computer systems, healthcare, manufacturing, project management, justice systems, and so on. Unlike the conventional queueing networks, fork-join processing networks have synchronization constraints that arise because of the parallel processing of tasks and can cause significant job delays. We study scheduling in fork-join processing networks with multiple job types and parallel shared resources. Jobs arriving in the system fork into arbitrary number of tasks, then those tasks are processed in parallel, and then they join and leave the network. There are shared resources processing multiple job types. We study the scheduling problem for those shared resources (i.e., which type of job to prioritize at any given time) and propose an asymptotically optimal scheduling policy in diffusion scale.