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An Algebraic Circuit for a multivariate polynomial P is a computational model for constructing the polynomial P using only additions and multiplications. It is a syntactic model of computation, as opposed to the Boolean Circuit model, and hence lower bounds for this model are widely expected to be easier to prove than lower bounds for Boolean circuits. Despite this, we do not have superpolynomial lower bounds against general algebraic circuits of depth 3 (except over constant-sized finite fields) and depth 4 (over any field other than F2), while constant-depth Boolean circuit lower bounds have been known since the early 1980s. In this paper, we prove the first superpolynomial lower bounds against algebraic circuits of all constant depths over all fields of characteristic 0. We also observe that our super-polynomial lower bound for constant-depth circuits implies the first deterministic sub-exponential time algorithm for solving the Polynomial Identity Testing (PIT) problem for all small-depth circuits using the known connection between algebraic hardness and randomness. [ABSTRACT FROM AUTHOR]

The paper discusses algorithmic priority inversion in mission-critical machine inference pipelines used in modern neural-network-based perception subsystems and describes a solution to mitigate its effect. In general, priority inversion occurs in computing systems when computations that are "less important" are performed together with or ahead of those that are "more important." Significant priority inversion occurs in existing machine inference pipelines when they do not differentiate between critical and less critical data. We describe a framework to resolve this problem and demonstrate that it improves a perception system's ability to react to critical inputs, while at the same time reducing platform cost. [ABSTRACT FROM AUTHOR]

The article discusses a research paper that applies online resource allocation algorithms to refugee resettlement, aiming to improve refugees' integration into local communities and employment prospects. By utilizing concepts from algorithm design, such as balancing resource utilization and maintaining capacity for future refugees, the authors were able to enhance the employability metric for resettlement agencies like the Hebrew Immigrant Aid Society (HIAS) by approximately 10%. This research not only addresses critical societal issues but also highlights the potential of algorithms to positively impact real-world outcomes for vulnerable populations, encouraging collaboration between algorithm designers and practitioners on important societal problems.

Recommender systems personalize content by recommending items to users. Item recommendation algorithms are evaluated by metrics that compare the positions of truly relevant items among the recommended items. To speed up the computation of metrics, recent work often uses sampled metrics where only a smaller set of random items and the relevant items are ranked. This paper investigates such sampled metrics in more detail and shows that they are inconsistent with their exact counterpart, in the sense that they do not persist relative statements, for example, recommender A is better than B, not even in expectation. Moreover, the smaller the sample size, the less difference there is between metrics, and for very small sample size, all metrics collapse to the AUC metric. We show that it is possible to improve the quality of the sampled metrics by applying a correction, obtained by minimizing different criteria. We conclude with an empirical evaluation of the naive sampled metrics and their corrected variants. To summarize, our work suggests that sampling should be avoided for metric calculation, however if an experimental study needs to sample, the proposed corrections can improve the quality of the estimate. [ABSTRACT FROM AUTHOR]

The Burrows-Wheeler Transform (BWT) is an invertible text transformation that permutes symbols of a text according to the lexicographical order of its suffixes. BWT is the main component of popular lossless compression programs (such as bzip2) as well as recent powerful compressed indexes (such as the r-index7), central in modern bioinformatics. The compressibility of BWT is quantified by the number r of equal-letter runs in the output. Despite the practical significance of BWT, no nontrivial upper bound on r is known. By contrast, the sizes of nearly all other known compression methods have been shown to be either always within a polylog n factor (where n is the length of the text) from z, the size of Lempel--Ziv (LZ77) parsing of the text, or much larger in the worst case (by an nε factor for ε > 0). In this paper, we show that r = O (z log² n) holds for every text. This result has numerous implications for text indexing and data compression; in particular: (1) it proves that many results related to BWT automatically apply to methods based on LZ77, for example, it is possible to obtain functionality of the suffix tree in O (z polylog n) space; (2) it shows that many text processing tasks can be solved in the optimal time assuming the text is compressible using LZ77 by a sufficiently large polylog n factor; and (3) it implies the first nontrivial relation between the number of runs in the BWT of the text and of its reverse. In addition, we provide an O (z polylog n)-time algorithm converting the LZ77 parsing into the run-length compressed BWT. To achieve this, we develop several new data structures and techniques of independent interest. In particular, we define compressed string synchronizing sets (generalizing the recently introduced powerful technique of string synchronizing sets11) and show how to efficiently construct them. Next, we propose a new variant of wavelet trees for sequences of long strings, establish a nontrivial bound on their size, and describe efficient construction algorithms. Finally, we develop new indexes that can be constructed directly from the LZ77 parsing and efficiently support pattern matching queries on text substrings. [ABSTRACT FROM AUTHOR]

In this paper, we describe multi-itinerary optimization (MIO)--a novel Bing Maps service that automates the process of building itineraries for multiple agents while optimizing their routes to minimize travel time or distance. MIO can be used by organizations with a fleet of vehicles and drivers, mobile salesforce, or a team of personnel in the field, to maximize workforce efficiency. It supports a variety of constraints, such as service time windows, duration, priority, pickup and delivery dependencies, and vehicle capacity. MIO also considers traffic conditions between locations, resulting in algorithmic challenges at multiple levels (e.g., calculating time-dependent travel-time distance matrices at scale and scheduling services for multiple agents). To support an end-to-end cloud service with turnaround times of a few seconds, our algorithm design targets a sweet spot between accuracy and performance. Toward that end, we build a scalable approach based on the ALNS metaheuristic. Our experiments show that accounting for traffic significantly improves solution quality: MIO finds efficient routes that avoid late arrivals, whereas traffic-agnostic approaches result in a 15% increase in the combined travel time and the lateness of an arrival. Furthermore, our approach generates itineraries with substantially higher quality than a cutting-edge heuristic (LKH), with faster running times for large instances. [ABSTRACT FROM AUTHOR]

The article addresses the topic of algorithm design in the solid-state drive (SSD) model of computation, noting its limitations as well as its benefits. The author references an accompanying paper which addresses one shortcoming in particular -- the phenomenon of "write amplification" -- by proposing a more accurate theoretical model of SSDs that incorporates read, write and erase operations.