Related papers: Compact Distributed Certification of Planar Graphs
Graph and network visualization supports exploration, analysis and communication of relational data arising in many domains: from biological and social networks, to transportation and powergrid systems. With the arrival of AI-based…
We consider labeling nodes of a directed graph for reachability queries. A reachability labeling scheme for such a graph assigns a binary string, called a label, to each node. Then, given the labels of nodes $u$ and $v$ and no other…
In the Partially Embedded Planarity problem, we are given a graph $G$ together with a topological drawing of a subgraph $H$ of $G$. The task is to decide whether the drawing can be extended to a drawing of the whole graph such that no two…
Verifying the complex and multi-step reasoning of Large Language Models (LLMs) is a critical challenge, as holistic methods often overlook localized flaws. Step-by-step validation is a promising alternative, yet existing methods are often…
Graph-based interactive theorem provers offer a visual representation of proofs, explicitly representing the dependencies and inferences between each of the proof steps in a graph or hypergraph format. The number and complexity of these…
This paper presents an analytical framework to model fault-tolerance in unstructured peer-to-peer overlays, represented as complex networks. We define a distributed protocol peers execute for managing the overlay and reacting to node…
We describe a protocol for creating, updating, and revoking digital diplomas that we anticipate would make use of the protocol for transferring digital assets elaborated by Goodell, Toliver, and Nakib. Digital diplomas would maintain their…
We introduce and study the problem \mpd, which asks for two planar graphs $G_1$ and $G_2$ whether $G_1$ can be embedded such that its dual is isomorphic to $G_2$. Our algorithmic main result is an NP-completeness proof for the general case…
Distributed protocols are generally parametric and can be executed on a system with any number of nodes, and hence proving their correctness becomes an infinite state verification problem. The most popular approach for verifying distributed…
We present a binary routing tree protocol for distributed hash table overlays. Using this protocol each peer can independently route messages to its parent and two descendants on the fly without any maintenance, global context, and…
The graph model checking problem consists in testing whether an input graph satisfies a given logical formula. In this paper, we study this problem in a distributed setting, namely local certification. The goal is to assign labels to the…
While SDNs enable more flexible and adaptive network operations, (logically) centralized reconfigurations introduce overheads and delays, which can limit network reactivity. This paper initiates the study of a more distributed approach, in…
We introduce and study the {\em orderly spanning trees} of plane graphs. This algorithmic tool generalizes {\em canonical orderings}, which exist only for triconnected plane graphs. Although not every plane graph admits an orderly spanning…
Let G be a plane graph of n nodes, m edges, f faces, and no self-loop. G need not be connected or simple (i.e., free of multiple edges). We give three sets of coding schemes for G which all take O(m+n) time for encoding and decoding. Our…
IC-planar graphs are those graphs that admit a drawing where no two crossed edges share an end-vertex and each edge is crossed at most once. They are a proper subfamily of the 1-planar graphs. Given an embedded IC-planar graph $G$ with $n$…
It is proven that a connected graph is planar if and only if all its cocycles with at least four edges are "grounded" in the graph. The notion of grounding of this planarity criterion, which is purely combinatorial, stems from the intuitive…
Verifying graph algorithms has long been considered challenging in separation logic, mainly due to structural sharing between graph subcomponents. We show that these challenges can be effectively addressed by representing graphs as a…
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,…
With the ever growing Internet of Things (IoT) market, ledger systems are facing new challenges to efficiently store and secure enormous customer records collected by the IoT devices. The authenticity, availability, and integrity of these…
In an emerging computing paradigm, computational capabilities, from processing power to storage capacities, are offered to users over communication networks as a cloud-based service. There, demanding computations are outsourced in order to…