arXiv subjects

Yuval Gil

Publications and source records attributed to Yuval Gil.

8 recordsLinked to original sources

arXiv2026

Online Algorithms with Unreliable Guidance

This paper introduces online algorithms with unreliable guidance (OAG), a model for ML-augmented online decision-making that cleanly separates the predictive and algorithmic components, thus offering a single, well-defined analysis framework that depends only on the problem at hand. Formulated through the lens of request-answer games, the OAG model brings multiple concepts (predictions from the answer space, guide, anytime competitiveness) which enable learning-augmented algorithms to be analyzed independently of predictor-specific choices - such as prediction semantics, error functions, or probing strategies - that would otherwise restrict the algorithm's generality and applicability. The clean framework of the OAG model allows to build the first generic compiler, the drop-or-trust-blindly (DTB) compiler, that turns almost any standard, prediction-free online algorithm into a learning-augmented one. Although simple, we show that the DTB compiler produces new learning-augmented algorithms with strong consistency-robustness guarantees for three classic online problems: we achieve new trade-offs for bipartite matching with adversarial arrival order, and obtain optimal solutions for caching and uniform metrical task systems.

cs.AI↗

arXiv2025

Distributed Interactive Proofs for Planarity with Log-Star Communication

We provide new communication-efficient distributed interactive proofs for planarity. The notion of a \emph{distributed interactive proof (DIP)} was introduced by Kol, Oshman, and Saxena (PODC 2018). In a DIP, the \emph{prover} is a single centralized entity whose goal is to prove a certain claim regarding an input graph $G$. To do so, the prover communicates with a distributed \emph{verifier} that operates concurrently on all $n$ nodes of $G$. A DIP is measured by the amount of prover-verifier communication it requires. Namely, the goal is to design a DIP with a small number of interaction rounds and a small \emph{proof size}, i.e., a small amount of communication per round. Our main result is an $O(\log ^{*}n)$-round DIP protocol for embedded planarity and planarity with a proof size of $O(1)$ and $O(\lceil\log \Delta/\log ^{*}n\rceil)$, respectively. In fact, this result can be generalized as follows. For any $1\leq r\leq \log^{*}n$, there exists an $O(r)$-round protocol for embedded planarity and planarity with a proof size of $O(\log ^{(r)}n)$ and $O(\log ^{(r)}n+\log \Delta /r)$, respectively.

cs.DC↗

arXiv2025

New Distributed Interactive Proofs for Planarity: A Matter of Left and Right

We provide new distributed interactive proofs (DIP) for planarity and related graph families. The notion of a \emph{distributed interactive proof} (DIP) was introduced by Kol, Oshman, and Saxena (PODC 2018). In this setting, the verifier consists of $n$ nodes connected by a communication graph $G$. The prover is a single entity that communicates with all nodes by short messages. The goal is to verify that the graph $G$ satisfies a certain property (e.g., planarity) in a small number of rounds, and with a small communication bound, denoted as the \emph{proof size}. Prior work by Naor, Parter and Yogev (SODA 2020) presented a DIP for planarity that uses three interaction rounds and a proof size of $O(\log n)$. Feuilloley et al.\ (PODC 2020) showed that the same can be achieved with a single interaction round and without randomization, by providing a proof labeling scheme with a proof size of $O(\log n)$. In a subsequent work, Bousquet, Feuilloley, and Pierron (OPODIS 2021) achieved the same bound for related graph families such as outerplanarity, series-parallel graphs, and graphs of treewidth at most $2$. In this work, we design new DIPs that use exponentially shorter proofs compared to the state-of-the-art bounds.

cs.DS↗

arXiv2024

On the Power of Graphical Reconfigurable Circuits

We introduce the \emph{graphical reconfigurable circuits (GRC)} model as an abstraction for distributed graph algorithms whose communication scheme is based on local mechanisms that collectively construct long-range reconfigurable channels (this is an extension to general graphs of a distributed computational model recently introduced by Feldmann et al.\ (JCB 2022) for hexagonal grids). The crux of the GRC model lies in its modest assumptions: (1) the individual nodes are computationally weak, with state space bounded independently of any global graph parameter; and (2) the reconfigurable communication channels are highly restrictive, only carrying information-less signals (a.k.a.\ \emph{beeps}). Despite these modest assumptions, we prove that GRC algorithms can solve many important distributed tasks efficiently, i.e., in polylogarithmic time. On the negative side, we establish various runtime lower bounds, proving that for other tasks, GRC algorithms (if they exist) are doomed to be slow.

cs.DC↗

arXiv2024

Improved Deterministic Distributed Maximum Weight Independent Set Approximation in Sparse Graphs

We design new deterministic CONGEST approximation algorithms for \emph{maximum weight independent set (MWIS)} in \emph{sparse graphs}. As our main results, we obtain new $\Delta(1+\epsilon)$-approximation algorithms as well as algorithms whose approximation ratio depend strictly on $\alpha$, in graphs with maximum degree $\Delta$ and arboricity $\alpha$. For (deterministic) $\Delta(1+\epsilon)$-approximation, the current state-of-the-art is due to a recent breakthrough by Faour et al.\ [SODA 2023] that showed an $O(\log^{2} (\Delta W)\cdot \log (1/\epsilon)+\log ^{*}n)$-round algorithm, where $W$ is the largest node-weight (this bound translates to $O(\log^{2} n\cdot\log (1/\epsilon))$ under the common assumption that $W=\text{poly}(n)$). As for $\alpha$-dependent approximations, a deterministic CONGEST $(8(1+\epsilon)\cdot\alpha)$-approximation algorithm with runtime $O(\log^{3} n\cdot\log (1/\epsilon))$ can be derived by combining the aforementioned algorithm of Faour et al.\ with a method presented by Kawarabayashi et al.\ [DISC 2020].

cs.DS↗

arXiv2023

Online Algorithms with Randomly Infused Advice

We introduce a novel method for the rigorous quantitative evaluation of online algorithms that relaxes the "radical worst-case" perspective of classic competitive analysis. In contrast to prior work, our method, referred to as randomly infused advice (RIA), does not make any probabilistic assumptions about the input sequence and does not rely on the development of designated online algorithms. Rather, it can be applied to existing online randomized algorithms, introducing a means to evaluate their performance in scenarios that lie outside the radical worst-case regime. More concretely, an online algorithm ALG with RIA benefits from pieces of advice generated by an omniscient but not entirely reliable oracle. The crux of the new method is that the advice is provided to ALG by writing it into the buffer B from which ALG normally reads its random bits, hence allowing us to augment it through a very simple and non-intrusive interface. The (un)reliability of the oracle is captured via a parameter 0 {\le} {\alpha} {\le} 1 that determines the probability (per round) that the advice is successfully infused by the oracle; if the advice is not infused, which occurs with probability 1 - {\alpha}, then the buffer B contains fresh random bits (as in the classic online setting). The applicability of the new RIA method is demonstrated by applying it to three extensively studied online problems: paging, uniform metrical task systems, and online set cover. For these problems, we establish new upper bounds on the competitive ratio of classic online algorithms that improve as the infusion parameter {\alpha} increases. These are complemented with (often tight) lower bounds on the competitive ratio of online algorithms with RIA for the three problems.

cs.DS↗

arXiv2022

Locally Restricted Proof Labeling Schemes (Full Version)

Introduced by Korman, Kutten, and Peleg (PODC 2005), a proof labeling scheme (PLS) is a distributed verification system dedicated to evaluating if a given configured graph satisfies a certain property. It involves a centralized prover, whose role is to provide proof that a given configured graph is a yes-instance by means of assigning labels to the nodes, and a distributed verifier, whose role is to verify the validity of the given proof via local access to the assigned labels. In this paper, we introduce the notion of a locally restricted PLS in which the prover's power is restricted to that of a LOCAL algorithm with a polylogarithmic number of rounds. To circumvent inherent impossibilities of PLSs in the locally restricted setting, we turn to models that relax the correctness requirements by allowing the verifier to accept some no-instances as long as they are not "too far" from satisfying the property in question. To this end, we evaluate (1) distributed graph optimization problems (OptDGPs) based on the notion of an approximate proof labeling scheme (APLS) (analogous to the type of relaxation used in sequential approximation algorithms); and (2) configured graph families (CGFs) based on the notion of atesting proof labeling schemes (TPLS) (analogous to the type of relaxation used in property testing algorithms).

cs.DC↗

arXiv2020

Twenty-Two New Approximate Proof Labeling Schemes (Full Version)

Introduced by Korman, Kutten, and Peleg (Distributed Computing 2005), a \emph{proof labeling scheme (PLS)} is a system dedicated to verifying that a given configuration graph satisfies a certain property. It is composed of a centralized \emph{prover}, whose role is to generate a proof for yes-instances in the form of an assignment of labels to the nodes, and a distributed \emph{verifier}, whose role is to verify the validity of the proof by local means and accept it if and only if the property is satisfied. To overcome lower bounds on the label size of PLSs for certain graph properties, Censor-Hillel, Paz, and Perry (SIROCCO 2017) introduced the notion of an \emph{approximate proof labeling scheme (APLS)} that allows the verifier to accept also some no-instances as long as they are not "too far" from satisfying the property.

cs.DC↗