TY - GEN

T1 - Deterministic Fault-Tolerant Connectivity Labeling Scheme

AU - Izumi, Taisuke

AU - Emek, Yuval

AU - Wadayama, Tadashi

AU - Masuzawa, Toshimitsu

N1 - Publisher Copyright:
© 2023 Owner/Author(s).

PY - 2023/6/19

Y1 - 2023/6/19

N2 - The f-fault-tolerant connectivity labeling (f-FTC labeling) is a scheme of assigning each vertex and edge with a small-size label such that one can determine the connectivity of two vertices s and t under the presence of at most f faulty edges only from the labels of s, t, and the faulty edges. This paper presents a new deterministic f-FTC labeling scheme attaining O(f2 polylog(n))-bit label size and a polynomial construction time, which settles the open problem left by Dory and Parter [18]. The key ingredient of our construction is to develop a deterministic counterpart of the graph sketch technique by Ahn, Guha, and McGreger [4], via some natural connection with the theory of error-correcting codes. This technique removes one major obstacle in de-randomizing the Dory-Parter scheme. The whole scheme is obtained by combining this technique with a new deterministic graph sparsification algorithm derived from the seminal ϵ-net theory, which is also of independent interest. As byproducts, our result deduces the first deterministic fault-tolerant approximate distance labeling scheme with a non-trivial performance guarantee and an improved deterministic fault-tolerant compact routing. The authors believe that our new technique is potentially useful in the future exploration of more efficient FTC labeling schemes and other related applications based on graph sketches.

AB - The f-fault-tolerant connectivity labeling (f-FTC labeling) is a scheme of assigning each vertex and edge with a small-size label such that one can determine the connectivity of two vertices s and t under the presence of at most f faulty edges only from the labels of s, t, and the faulty edges. This paper presents a new deterministic f-FTC labeling scheme attaining O(f2 polylog(n))-bit label size and a polynomial construction time, which settles the open problem left by Dory and Parter [18]. The key ingredient of our construction is to develop a deterministic counterpart of the graph sketch technique by Ahn, Guha, and McGreger [4], via some natural connection with the theory of error-correcting codes. This technique removes one major obstacle in de-randomizing the Dory-Parter scheme. The whole scheme is obtained by combining this technique with a new deterministic graph sparsification algorithm derived from the seminal ϵ-net theory, which is also of independent interest. As byproducts, our result deduces the first deterministic fault-tolerant approximate distance labeling scheme with a non-trivial performance guarantee and an improved deterministic fault-tolerant compact routing. The authors believe that our new technique is potentially useful in the future exploration of more efficient FTC labeling schemes and other related applications based on graph sketches.

KW - fault-tolerant data structure

KW - graph connectivity

KW - labeling scheme

UR - http://www.scopus.com/inward/record.url?scp=85163987063&partnerID=8YFLogxK

U2 - 10.1145/3583668.3594584

DO - 10.1145/3583668.3594584

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AN - SCOPUS:85163987063

T3 - Proceedings of the Annual ACM Symposium on Principles of Distributed Computing

SP - 190

EP - 199

BT - PODC 2023 - Proceedings of the 2023 ACM Symposium on Principles of Distributed Computing

T2 - 42nd ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, PODC 2023

Y2 - 19 June 2023 through 23 June 2023

ER -