Dynamic "Succincter"

Augmented B-trees (aB-trees) are a broad class of data structures. The seminal work "succincter" by Patrascu showed that any aB-tree can be stored using only two bits of redundancy, while supporting queries to the tree in time proportional to its depth. It has been a versatile building block for constructing succinct data structures, including rank/select data structures, dictionaries, locally decodable arithmetic coding, storing balanced parenthesis, etc. In this paper, we show how to "dynamize" an aB-tree. Our main result is the design of dynamic aB-trees (daB-trees) with branching factor two using only three bits of redundancy (with the help of lookup tables that are of negligible size in applications), while supporting updates and queries in time polynomial in its depth. As an application, we present a dynamic rank/select data structure for $n$-bit arrays, also known as a dynamic fully indexable dictionary (FID). It supports updates and queries in $O(\log n/\log\log n)$ time, and when the array has $m$ ones, the data structure occupies $$\log\binom{n}{m} + O(n/2^{\log^{0.199}n})$$ bits. Note that the update and query times are optimal even without space constraints due to a lower bound by Fredman and Saks. Prior to our work, no dynamic FID with near-optimal update and query times and redundancy $o(n/\log n)$ was known. We further show that a dynamic sequence supporting insertions, deletions and rank/select queries can be maintained in (optimal) $O(\log n/\log\log n)$ time and with $O(n \cdot \text{poly}\log\log n/\log^2 n)$ bits of redundancy.Comment: 33 pages, 1 figure; in FOCS 202

Dynamic Dictionary with Subconstant Wasted Bits per Key

Dictionaries have been one of the central questions in data structures. A dictionary data structure maintains a set of key-value pairs under insertions and deletions such that given a query key, the data structure efficiently returns its value. The state-of-the-art dictionaries [Bender, Farach-Colton, Kuszmaul, Kuszmaul, Liu 2022] store $n$ key-value pairs with only $O(n \log^{(k)} n)$ bits of redundancy, and support all operations in $O(k)$ time, for $k \leq \log^* n$. It was recently shown to be optimal [Li, Liang, Yu, Zhou 2023b]. In this paper, we study the regime where the redundant bits is $R=o(n)$, and show that when $R$ is at least $n/\text{poly}\log n$, all operations can be supported in $O(\log^* n + \log (n/R))$ time, matching the lower bound in this regime [Li, Liang, Yu, Zhou 2023b]. We present two data structures based on which range $R$ is in. The data structure for $R<n/\log^{0.1} n$ utilizes a generalization of adapters studied in [Berger, Kuszmaul, Polak, Tidor, Wein 2022] and [Li, Liang, Yu, Zhou 2023a]. The data structure for $R \geq n/\log^{0.1} n$ is based on recursively hashing into buckets with logarithmic sizes.Comment: 46 pages; SODA 202

Tight Cell-Probe Lower Bounds for Dynamic Succinct Dictionaries

A dictionary data structure maintains a set of at most $n$ keys from the universe $[U]$ under key insertions and deletions, such that given a query $x \in [U]$, it returns if $x$ is in the set. Some variants also store values associated to the keys such that given a query $x$, the value associated to $x$ is returned when $x$ is in the set. This fundamental data structure problem has been studied for six decades since the introduction of hash tables in 1953. A hash table occupies $O(n\log U)$ bits of space with constant time per operation in expectation. There has been a vast literature on improving its time and space usage. The state-of-the-art dictionary by Bender, Farach-Colton, Kuszmaul, Kuszmaul and Liu [BFCK+22] has space consumption close to the information-theoretic optimum, using a total of $$\log\binom{U}{n}+O(n\log^{(k)} n)$$ bits, while supporting all operations in $O(k)$ time, for any parameter $k \leq \log^* n$. The term $O(\log^{(k)} n) = O(\underbrace{\log\cdots\log}_k n)$ is referred to as the wasted bits per key. In this paper, we prove a matching cell-probe lower bound: For $U=n^{1+\Theta(1)}$, any dictionary with $O(\log^{(k)} n)$ wasted bits per key must have expected operational time $\Omega(k)$, in the cell-probe model with word-size $w=\Theta(\log U)$. Furthermore, if a dictionary stores values of $\Theta(\log U)$ bits, we show that regardless of the query time, it must have $\Omega(k)$ expected update time. It is worth noting that this is the first cell-probe lower bound on the trade-off between space and update time for general data structures.Comment: 35 page

On the Perturbation Function of Ranking and Balance for Weighted Online Bipartite Matching

Ranking and Balance are arguably the two most important algorithms in the online matching literature. They achieve the same optimal competitive ratio of 1-1/e for the integral version and fractional version of online bipartite matching by Karp, Vazirani, and Vazirani (STOC 1990) respectively. The two algorithms have been generalized to weighted online bipartite matching problems, including vertex-weighted online bipartite matching and AdWords, by utilizing a perturbation function. The canonical choice of the perturbation function is f(x) = 1-e^{x-1} as it leads to the optimal competitive ratio of 1-1/e in both settings. We advance the understanding of the weighted generalizations of Ranking and Balance in this paper, with a focus on studying the effect of different perturbation functions. First, we prove that the canonical perturbation function is the unique optimal perturbation function for vertex-weighted online bipartite matching. In stark contrast, all perturbation functions achieve the optimal competitive ratio of 1-1/e in the unweighted setting. Second, we prove that the generalization of Ranking to AdWords with unknown budgets using the canonical perturbation function is at most 0.624 competitive, refuting a conjecture of Vazirani (2021). More generally, as an application of the first result, we prove that no perturbation function leads to the prominent competitive ratio of 1-1/e by establishing an upper bound of 1-1/e-0.0003. Finally, we propose the online budget-additive welfare maximization problem that is intermediate between AdWords and AdWords with unknown budgets, and we design an optimal 1-1/e competitive algorithm by generalizing Balance

AN EVALUATION OF THE POOLED LOLLI-METHOD RT-qPCR TESTING FOR COVID-19 SURVEILLANCE IN SINGAPORE

Background: Following the success of the Lolli-Method or Lolli-Test as a surveillance method in Germany, the Ministry of Health, Singapore investigated the feasibility of deploying the method as a rostered routine testing in vulnerable individuals such as children, nursing homes and frontline workers; and evaluated the sensitivity and ideal pooling ratio of the Lolli-Method.&nbsp; Methods: The study was conducted in two phases – the first phase was to assess the operational feasibility of the Lolli-Method. It was held in conjunction with air sampling at a childcare centre with children ages 2 to 6 years old across 40 days. The second phase was to evaluate the sensitivity of the Lolli-Method with different pooling ratios and was conducted in collaboration with the National Centre for Infectious Diseases (NCID) where each pool was spiked with one Lolli swab from a COVID-positive patient. All patients enrolled in this study have their viral load cycle threshold (CT) levels assessed prior to admission via a mid-turbinate oropharyngeal (MTOP) polymerase chain reaction (PCR) swab.&nbsp; Results: The sensitivity of the pooled Lolli-Test was similar to antigen rapid tests with 100% sensitivity (3/3) in a pooling ratio of 20:1 for patients with viral loads of cycle threshold (CT) levels below 20. For individuals with lower viral loads, the sensitivity of the Lolli-Test was 66.7% (2/3) in a pooling ratio of 20:1 and 100% (2/2) in a smaller pooling ratio of 15:1. The operational feasibility of the Lolli-Test was assessed to be high amongst study participants although students were noted to require some additional assistance from teachers.&nbsp; Conclusion: The Lolli-Test is an effective surveillance method with adequate sensitivity to detect a COVID-19 infected individual in a pool of up to 20 albeit largely dependent on the viral load. Furthermore, the Lolli-Test also provides a less invasive alternative sample collection method for individuals who cannot tolerate or have contraindications for the regular nasal or oropharyngeal swabs such as young children. More studies should be done to assess the Lolli-Test’s true limit of detection and to evaluate the use of the Lolli-Method in infants and for other respiratory diseases such as influenza

Aridity-driven shift in biodiversity–soil multifunctionality relationships

From Springer Nature via Jisc Publications RouterHistory: received 2021-01-07, accepted 2021-08-12, registration 2021-08-25, pub-electronic 2021-09-09, online 2021-09-09, collection 2021-12Publication status: PublishedFunder: National Natural Science Foundation of China (National Science Foundation of China); doi: https://doi.org/10.13039/501100001809; Grant(s): 31770430Abstract: Relationships between biodiversity and multiple ecosystem functions (that is, ecosystem multifunctionality) are context-dependent. Both plant and soil microbial diversity have been reported to regulate ecosystem multifunctionality, but how their relative importance varies along environmental gradients remains poorly understood. Here, we relate plant and microbial diversity to soil multifunctionality across 130 dryland sites along a 4,000 km aridity gradient in northern China. Our results show a strong positive association between plant species richness and soil multifunctionality in less arid regions, whereas microbial diversity, in particular of fungi, is positively associated with multifunctionality in more arid regions. This shift in the relationships between plant or microbial diversity and soil multifunctionality occur at an aridity level of ∼0.8, the boundary between semiarid and arid climates, which is predicted to advance geographically ∼28% by the end of the current century. Our study highlights that biodiversity loss of plants and soil microorganisms may have especially strong consequences under low and high aridity conditions, respectively, which calls for climate-specific biodiversity conservation strategies to mitigate the effects of aridification

On the Perturbation Function of Ranking and Balance for Weighted Online Bipartite Matching

Ranking and Balance are arguably the two most important algorithms in the online matching literature. They achieve the same optimal competitive ratio of $1-1/e$ for the integral version and fractional version of online bipartite matching by Karp, Vazirani, and Vazirani (STOC 1990) respectively. The two algorithms have been generalized to weighted online bipartite matching problems, including vertex-weighted online bipartite matching and AdWords, by utilizing a perturbation function. The canonical choice of the perturbation function is $f(x)=1-e^{x-1}$ as it leads to the optimal competitive ratio of $1-1/e$ in both settings. We advance the understanding of the weighted generalizations of Ranking and Balance in this paper, with a focus on studying the effect of different perturbation functions. First, we prove that the canonical perturbation function is the \emph{unique} optimal perturbation function for vertex-weighted online bipartite matching. In stark contrast, all perturbation functions achieve the optimal competitive ratio of $1-1/e$ in the unweighted setting. Second, we prove that the generalization of Ranking to AdWords with unknown budgets using the canonical perturbation function is at most $0.624$ competitive, refuting a conjecture of Vazirani (2021). More generally, as an application of the first result, we prove that no perturbation function leads to the prominent competitive ratio of $1-1/e$ by establishing an upper bound of $1-1/e-0.0003$. Finally, we propose the online budget-additive welfare maximization problem that is intermediate between AdWords and AdWords with unknown budgets, and we design an optimal $1-1/e$ competitive algorithm by generalizing Balance.Comment: Conference version to appear at the European Symposium on Algorithms (ESA 2023). 16 pages, 2 figures, 8 pages appendi

SAfeDJ : A crowd-cloud codesign approach to situation-aware music delivery for drivers

Driving is an integral part of our everyday lives, but it is also a time when people are uniquely vulnerable. Previous research has demonstrated that not only does listening to suitable music while driving not impair driving performance, but it could lead to an improved mood and a more relaxed body state, which could improve driving performance and promote safe driving significantly. In this article, we propose SAfeDJ, a smartphone-based situation-aware music recommendation system, which is designed to turn driving into a safe and enjoyable experience. SAfeDJ aims at helping drivers to diminish fatigue and negative emotion. Its design is based on novel interactive methods, which enable in-car smartphones to orchestrate multiple sources of sensing data and the drivers' social context, in collaboration with cloud computing to form a seamless crowdsensing solution. This solution enables different smartphones to collaboratively recommend preferable music to drivers according to each driver's specific situations in an automated and intelligent manner. Practical experiments of SAfeDJ have proved its effectiveness in music-mood analysis, and mood-fatigue detections of drivers with reasonable computation and communication overheads on smartphones. Also, our user studies have demonstrated that SAfeDJ helps to decrease fatigue degree and negative mood degree of drivers by 49.09% and 36.35%, respectively, compared to traditional smartphone-based music player under similar driving situations