Compact Routing on Planar Graphs
Notice bibliographique
Résumé
This thesis delves into the exploration of shortest path queries in planar graphs, with an emphasis on the utilization of space-efficient data structures. Our investigation primarily targets connected, undirected, static pointer planar graphs, focusing on scenarios where queries predominantly start or end at a select subset of nodes. \n \nThe shortest path problem, central to our study, boasts a rich historical context and has profound real-world implications in diverse fields such as web mapping, robotics, and VLSI circuit design. Our research is pivoted on the space-efficient representation of planar graphs, a critical consideration in 2D visualizations and city map representations. \n \nIn this thesis, shortest path queries are delineated into three categories: shortest path, distance oracle, and port queries, each with distinct computational characteristics and storage requirements. A significant portion of our research is focused on center-based configurations in graphs, where a small subset of nodes, designated as ‘centers,’ plays a pivotal role. These centers are crucial, either due to their strategic importance within the graph, which necessitates more prompt responses to queries, or due to their high frequency in the query list. We explore various scenarios within this configuration. Our approach prioritizes handling queries involving these centers more efficiently, aiming to provide rapid responses for strategically important queries and to enhance overall query processing speed. This method is particularly effective, as addressing the queries linked to these relatively few but significant centers can substantially improve the efficiency of the entire system. Such prioritization reflects practical applications like urban navigation, where focusing on key locations can significantly expedite overall navigation and operational efficiency. \n \nFor shortest path queries in a center-based configuration, we have developed a data structure that efficiently answers queries from other nodes to centers in O(length of the path) time. In the first scenario, where all queries are from or to a center, the space requirement is 3n+2m+2km+o(nk), where n represents the number of nodes, m the number of edges, and k the number of centers. Additionally, our approach supports distributed storage and processing, facilitating parallel computing. \n \nFor distance oracle queries in unweighted graphs within a center-based configuration, our methods manage responses in O(log^(1+ϵ) n) time with an additional o(nk) space requirement. In general, for unweighted graphs without any specific configuration, the distance oracle requires 2n + 2m + 2nm + o(n) bits of space, offering responses in a similar time frame. The strength of our approach lies in its distributability across multiple servers, which enhances concurrent query processing, a feature particularly beneficial in center-based configurations. \n \nMoreover, we introduce a specialized data structure for distributed routing tables, capable of responding to port queries in constant time. This structure efficiently utilizes space, limiting the aggregate bit requirement for all routing tables within graph G to 3.2n^2+o(n^2) bits.
Récupéré en direct depuis OpenAlex et désinversé. Les résumés ne sont pas conservés dans cette base de données : les index inversés représentent 8,6 Go des 9,3 Go de texte de la base, et le serveur dispose de 13 Go libres.
Comment cette classification a été obtenuedéplier
Prédiction machine sur la base complète
Imitation des enseignantsNi prévalence calibrée, ni vérité terrain. Validation humaine à venir. Le volet Gemma est une étiquette directe du modèle pour chaque travail de la base, lue sur la notice réduite au titre. Le volet Codex est un classifieur appris des 10 348 étiquettes directes de Codex et calibré sur les taux pondérés de l'échantillon; les champs sans appui suffisant ne portent aucun appel Codex. Le mode candidate est l'union des deux volets; le consensus est leur intersection. Ces sorties portent le statut machine_predicted_unvalidated et ne sont pas des étiquettes humaines.
Scores du classifieur distillé par catégorie (deux têtes)
| Catégorie | Codex | Gemma |
|---|---|---|
| Métarecherche | 0,000 | 0,004 |
| Méta-épidémiologie (sens strict) | 0,001 | 0,000 |
| Méta-épidémiologie (sens large) | 0,001 | 0,001 |
| Bibliométrie | 0,001 | 0,002 |
| Études des sciences et des technologies | 0,001 | 0,001 |
| Communication savante | 0,002 | 0,003 |
| Science ouverte | 0,001 | 0,002 |
| Intégrité de la recherche | 0,001 | 0,001 |
| Charge utile insuffisante (le modèle a refusé de juger) | 0,008 | 0,001 |
Scores machine (provisoires)
Les deux têtes enseignantes du modèle étudiant, lues sur ce travail. Un score ordonne la base pour la relecture; il n'affirme jamais une catégorie, et le statut de validation accompagne chaque rangée tel quel.
Scores de référence d'un modèle non mature (critères de maturité non atteints, 7 itérations). Un score ordonne; il n'affirme jamais une catégorie.
score_only:v0-immature-baseline · tel quel depuis la passe de notation : score_only signifie que le nombre peut ordonner les travaux, et qu'aucune étiquette de catégorie n'en découleClassification
machine, non validéePrédiction automatique; un appel candidat d’une seule source (Gemma direct ou Codex distillé), pas un consensus.
Le détail, modèle par modèle et score par score, se trouve en fin de page sous « Comment cette classification a été obtenue ».