Leonid Barenboim’s research while affiliated with The Open University of Israel and other places

The emergence of autonomous vehicles (AVs) marks a transformative leap in transportation technology. Central to the success of AVs is ensuring user safety, but this endeavor is accompanied by the challenge of establishing trust and acceptance of this novel technology. The traditional “one size fits all” approach to AVs may limit their broader societal, economic, and cultural impact. Here, we introduce the Persona-PhysioSync AV (PPS-AV). It adopts a comprehensive approach by combining personality traits with physiological and emotional indicators to personalize the AV experience to enhance trust and comfort. A significant aspect of the PPS-AV framework is its real-time monitoring of passenger engagement and comfort levels within AVs. It considers a passenger’s personality traits and their interaction with physiological and emotional responses. The framework can alert passengers when their engagement drops to critical levels or when they exhibit low situational awareness, ensuring they regain attentiveness promptly, especially during Take-Over Request (TOR) events. This approach fosters a heightened sense of Human–Vehicle Interaction (HVI), thereby building trust in AV technology. While the PPS-AV framework currently provides a foundational level of state diagnosis, future developments are expected to include interaction protocols that utilize interfaces like haptic alerts, visual cues, and auditory signals. In summary, the PPS-AV framework is a pivotal tool for the future of autonomous transportation. By prioritizing safety, comfort, and trust, it aims to make AVs not just a mode of transport but a personalized and trusted experience for passengers, accelerating the adoption and societal integration of autonomous vehicles.

We obtain improved distributed algorithms in the CONGEST message-passing setting for problems on power graphs of an input graph G. This includes Coloring, Maximal Independent Set, and related problems. We develop a general deterministic technique that transforms R-round algorithms for G with certain properties into $O(R \cdot \Delta^{k/2 - 1})$-round algorithms for $G^k$. This improves the previously-known running time for such transformation, which was $O(R \cdot \Delta^{k - 1})$. Consequently, for problems that can be solved by algorithms with the required properties and within polylogarithmic number of rounds, we obtain {quadratic} improvement for $G^k$ and {exponential} improvement for $G^2$. We also obtain significant improvements for problems with larger number of rounds in G.

We study algorithms in the LOCAL model that produce secured output. Specifically, each vertex computes its part in the output, the entire output is correct, but each vertex cannot discover the output of other vertices, with a certain probability. As the extensive research in the distributed algorithms field yielded efficient decentralized algorithms, the discussion about the security of distributed algorithms was somewhat neglected. Nevertheless, many protocols and algorithms were devised in the research area of secure multi-party computation problem. However, the focus in those protocols was to work for every function f at the expense of increasing the round complexity, or the necessity of several computational assumptions. We present a novel approach, which identifies and develops those algorithms that are inherently secure (which means they do not require any further constructions). This approach yields efficient secure algorithms for various labeling and decomposition problems without requiring any hardness assumption, but only a private randomness generator in each vertex.

We consider the Backup Placement problem in networks in the CONGEST distributed setting. Given a network graph G=(V,E), the goal of each vertex v∈V is selecting a neighbor, such that the maximum number of vertices in V that select the same vertex is minimized. The backup placement problem was introduced by Halldorsson, Kohler, Patt-Shamir, and Rawitz, who obtained in 2015 an O(logn/loglogn) approximation with randomized polylogarithmic time. Their algorithm remained state-of-the-art for general graphs, as well as for specific graph topologies. In the current paper, we obtain significantly improved algorithms for various graph topologies. Specifically, we show that O(1)-approximation to optimal backup placement can be computed deterministically in O(1) rounds (and even just one round) in wireless networks, certain social networks, claw-free graphs, and, more precisely, in any graph with neighborhood independence bounded by a constant. We also consider graphs such as trees, forests, planar graphs and, more precisely, graphs of constant arboricity. For such graphs, we obtain constant approximation to optimal backup placement in O(logn) deterministic rounds. Clearly, our constant-time algorithms for graphs with constant neighborhood independence are asymptotically optimal. Moreover, we show that our algorithms for graphs with constant arboricity are not far from optimal as well by proving several lower bounds. Specifically, in unoriented trees, optimal backup placement requires Ω(logn) time and polylogarithmic-approximate backup placement requires Ω(logn/loglogn) time. These lower bounds are applicable in particular to graphs of constant arboricity.

We consider graph coloring and related problems in the distributed message-passing model. Locally-iterative algorithms are especially important in this setting. These are algorithms in which each vertex decides about its next color only as a function of the current colors in its 1-hop-neighborhood . In STOC’93 Szegedy and Vishwanathan showed that any locally-iterative Δ + 1-coloring algorithm requires Ω (Δ log Δ + log * n ) rounds, unless there exists “a very special type of coloring that can be very efficiently reduced” [ 44 ]. No such special coloring has been found since then. This led researchers to believe that Szegedy-Vishwanathan barrier is an inherent limitation for locally-iterative algorithms and to explore other approaches to the coloring problem [ 2 , 3 , 19 , 32 ]. The latter gave rise to faster algorithms, but their heavy machinery that is of non-locally-iterative nature made them far less suitable to various settings. In this article, we obtain the aforementioned special type of coloring. Specifically, we devise a locally-iterative Δ + 1-coloring algorithm with running time O (Δ + log * n ), i.e., below Szegedy-Vishwanathan barrier. This demonstrates that this barrier is not an inherent limitation for locally-iterative algorithms. As a result, we also achieve significant improvements for dynamic, self-stabilizing, and bandwidth-restricted settings. This includes the following results: We obtain self-stabilizing distributed algorithms for Δ + 1-vertex-coloring, (2Δ - 1)-edge-coloring, maximal independent set, and maximal matching with O (Δ + log * n ) time. This significantly improves previously known results that have O(n) or larger running times [ 23 ]. We devise a (2Δ - 1)-edge-coloring algorithm in the CONGEST model with O (Δ + log * n ) time and O (Δ)-edge-coloring in the Bit-Round model with O (Δ + log n ) time. The factors of log * n and log n are unavoidable in the CONGEST and Bit-Round models, respectively. Previously known algorithms had superlinear dependency on Δ for (2Δ - 1)-edge-coloring in these models. We obtain an arbdefective coloring algorithm with running time O (√ Δ + log * n ). Such a coloring is not necessarily proper, but has certain helpful properties. We employ it to compute a proper (1 + ε)Δ-coloring within O (√ Δ + log * n ) time and Δ + 1-coloring within O (√ Δ log Δ log * Δ + log * n ) time. This improves the recent state-of-the-art bounds of Barenboim from PODC’15 [ 2 ] and Fraigniaud et al. from FOCS’16 [ 19 ] by polylogarithmic factors. Our algorithms are applicable to the SET-LOCAL model [ 25 ] (also known as the weak LOCAL model). In this model a relatively strong lower bound of Ω (Δ 1/3 ) is known for Δ + 1-coloring. However, most of the coloring algorithms do not work in this model. (In Reference [ 25 ] only Linial’s O (Δ ² )-time algorithm and Kuhn-Wattenhofer O (Δ log Δ)-time algorithms are shown to work in it.) We obtain the first linear-in-Δ Δ + 1-coloring algorithms that work also in this model.

We provide a deterministic scheme for solving any decidable problem in the distributed {sleeping model}. The sleeping model is a generalization of the standard message-passing model, with an additional capability of network nodes to enter a sleeping state occasionally. As long as a vertex is in the awake state, it is similar to the standard message-passing setting. However, when a vertex is asleep it cannot receive or send messages in the network nor can it perform internal computations. On the other hand, sleeping rounds do not count towards {\awake complexity.} Awake complexity is the main complexity measurement in this setting, which is the number of awake rounds a vertex spends during an execution. In this paper we devise algorithms with worst-case guarantees on the awake complexity. We devise a deterministic scheme with awake complexity of $O(\log n)$ for solving any decidable problem in this model by constructing a structure we call { Distributed Layered Tree}. This structure turns out to be very powerful in the sleeping model, since it allows one to collect the entire graph information within a constant number of awake rounds. Moreover, we prove that our general technique cannot be improved in this model, by showing that the construction of distributed layered trees itself requires $\Omega(\log n)$ awake rounds. Another result we obtain in this work is a deterministic scheme for solving any problem from a class of problems, denoted O-LOCAL, in $O(\log \Delta + \log^*n)$ awake rounds. This class contains various well-studied problems, such as MIS and $(\Delta+1)$-vertex-coloring.

Sensor nodes are inherently a cheap piece of hardware – due to the common need to use many of them over a large area – and usually contain a small amount of RAM and flash memory, which are insufficient in case of high degree of data sampling. An overloaded sensor can harm the data integrity, or even completely reject incoming messages. The problem gets even worse when data should be received from many nodes, as missing data becomes a more common phenomenon as deployed WSNs grow in scale. As a solution, we consider the Backup Placement problem in networks in the network management distributed setting: Given a network graph G = (V, E), the goal of each vertex v∈V is selecting a neighbor, such that the maximum number of vertices in V that select the same vertex is minimized. In cases of an overflow, our Distributed Adaptive Clustering algorithm (D-ACR) reconfigures the network, by adaptively and hierarchically re-clustering parts of it, based on the rate of incoming data packages in order to minimize the energy- consumption, and prevent premature death of nodes. In the network management setting of a grid, we proved that a backup placement of load at most O(1) can be maintained within O(log2 n) update time, and an O(n log2 n) energy consumption using the constructed ACR tree.