arXiv subjects

Jonathan Gal

Publications and source records attributed to Jonathan Gal.

4 recordsLinked to original sources

arXiv2026

Incremental Dominating Set

Dominating Set is a fundamental problem in graph theory: given a graph, find a minimum-weight subset of vertices such that every vertex is either selected or adjacent to a selected vertex. In online settings where vertices arrive sequentially, comparing algorithms against an offline optimum with full knowledge of the input leads to extremely strong lower bounds, where even a simple star graph shows that any online algorithm must have competitive ratio $\Omega(\Delta)$, with $\Delta$ the largest degree of any vertex in the graph, matching the trivial strategy of selecting all vertices. We study the incremental dominating set problem, where the optimal algorithm is constrained to the same choices available to online algorithms. This introduces a benchmark that enables a meaningful comparison between algorithms. We present the first results for vertex-weighted graphs and randomized algorithms in this model. For incremental dominating set, we give an $O(\Delta)$-competitive deterministic algorithm and an $O(\log^2\Delta)$-competitive randomized algorithm. We extend these results to the Connected Dominating Set problem using a linear-programming formulation that captures connectivity through local constraints. When the neighborhood of each arriving vertex is known \textit{in advance}, deterministic algorithms achieve similar polylogarithmic competitive ratios as their randomized counterparts. Finally, we establish matching lower bounds, showing that our results are optimal up to constant factors.

cs.DS↗

arXiv2025

Analyzing Deviations from Monotonic Trends through Database Repair

Datasets often exhibit violations of expected monotonic trends - for example, higher education level correlating with higher average salary, newer homes being more expensive, or diabetes prevalence increasing with age. We address the problem of quantifying how far a dataset deviates from such trends. To this end, we introduce Aggregate Order Dependencies (AODs), an aggregation-centric extension of the previously studied order dependencies. An AOD specifies that the aggregated value of a target attribute (e.g., mean salary) should monotonically increase or decrease with the grouping attribute (e.g., education level). We formulate the AOD repair problem as finding the smallest set of tuples to delete from a table so that the given AOD is satisfied. We analyze the computational complexity of this problem and propose a general algorithmic template for solving it. We instantiate the template for common aggregation functions, introduce optimization techniques that substantially improve the runtime of the template instances, and develop efficient heuristic alternatives. Our experimental study, carried out on both real-world and synthetic datasets, demonstrates the practical efficiency of the algorithms and provides insight into the performance of the heuristics. We also present case studies that uncover and explain unexpected AOD violations using our framework.

cs.DB↗

arXiv2023

Majority is not Needed: A Counterstrategy to Selfish Mining

In the last few years several papers investigated selfish mine attacks, most of which assumed that every miner that is not part of the selfish mine pool will continue to mine honestly. However, in reality, remaining honest is not always incentivized, particularly when another pool is employing selfish mining or other deviant strategies. In this work we explore the scenario in which a large enough pool capitalises on another selfish pool to gain 100\% of the profit and commit double spending attacks. We show that this counterstrategy can effectively counter any deviant strategy, and that even the possibility of it discourages other pools from implementing deviant strategies.

cs.CR↗

arXiv2022

AritPIM: High-Throughput In-Memory Arithmetic

Digital processing-in-memory (PIM) architectures are rapidly emerging to overcome the memory-wall bottleneck by integrating logic within memory elements. Such architectures provide vast computational power within the memory itself in the form of parallel bitwise logic operations. We develop novel algorithmic techniques for PIM that, combined with new perspectives on computer arithmetic, extend this bitwise parallelism to the four fundamental arithmetic operations (addition, subtraction, multiplication, and division), for both fixed-point and floating-point numbers, and using both bit-serial and bit-parallel approaches. We propose a state-of-the-art suite of arithmetic algorithms, demonstrating the first algorithm in the literature of digital PIM for a majority of cases - including cases previously considered impossible for digital PIM, such as floating-point addition. Through a case study on memristive PIM, we compare the proposed algorithms to an NVIDIA RTX 3070 GPU and demonstrate significant throughput and energy improvements.

cs.AR↗