TY - JOUR

T1 - Proof-labeling schemes

T2 - Broadcast, unicast and in between

AU - Patt-Shamir, Boaz

AU - Perry, Mor

N1 - Publisher Copyright:
© 2022 Elsevier B.V.

PY - 2022/6/26

Y1 - 2022/6/26

N2 - We study the effect of limiting the number of different messages a node can transmit simultaneously on the verification complexity of proof-labeling schemes (PLS). In a PLS, each node is given a label, and the goal is to verify, by exchanging messages over each link in each direction, that a certain global predicate is satisfied by the system configuration. We consider a single parameter r that bounds the number of distinct messages that can be sent concurrently by any node: in the case r=1, each node may only send the same message to all its neighbors (the broadcast model), in the case r≥Δ, where Δ is the largest node degree in the system, each neighbor may be sent a distinct message (the unicast model), and in general, for 1≤r≤Δ, each of the r messages is destined to a subset of the neighbors. We show that message compression linear in r is possible for verifying fundamental problems such as the agreement between edge endpoints on the edge state. Some problems, including verification of maximal matching, exhibit a large gap in complexity between r=1 and r>1. For some other important predicates, the verification complexity is insensitive to r, e.g., the question whether a subset of edges constitutes a spanning-tree. We also consider the congested clique model. We show that the crossing technique [1] for proving lower bounds on the verification complexity can be applied in the case of congested clique only if r=1. Together with a new upper bound, this allows us to determine the verification complexity of MST in the broadcast clique. Finally, we establish a general connection between the deterministic and randomized verification complexity for any given number r.

AB - We study the effect of limiting the number of different messages a node can transmit simultaneously on the verification complexity of proof-labeling schemes (PLS). In a PLS, each node is given a label, and the goal is to verify, by exchanging messages over each link in each direction, that a certain global predicate is satisfied by the system configuration. We consider a single parameter r that bounds the number of distinct messages that can be sent concurrently by any node: in the case r=1, each node may only send the same message to all its neighbors (the broadcast model), in the case r≥Δ, where Δ is the largest node degree in the system, each neighbor may be sent a distinct message (the unicast model), and in general, for 1≤r≤Δ, each of the r messages is destined to a subset of the neighbors. We show that message compression linear in r is possible for verifying fundamental problems such as the agreement between edge endpoints on the edge state. Some problems, including verification of maximal matching, exhibit a large gap in complexity between r=1 and r>1. For some other important predicates, the verification complexity is insensitive to r, e.g., the question whether a subset of edges constitutes a spanning-tree. We also consider the congested clique model. We show that the crossing technique [1] for proving lower bounds on the verification complexity can be applied in the case of congested clique only if r=1. Together with a new upper bound, this allows us to determine the verification complexity of MST in the broadcast clique. Finally, we establish a general connection between the deterministic and randomized verification complexity for any given number r.

KW - CONGEST model

KW - Congested clique

KW - Proof-labeling schemes

KW - Verification complexity

UR - http://www.scopus.com/inward/record.url?scp=85131420962&partnerID=8YFLogxK

U2 - 10.1016/j.tcs.2022.05.006

DO - 10.1016/j.tcs.2022.05.006

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AN - SCOPUS:85131420962

SN - 0304-3975

VL - 923

SP - 179

EP - 195

JO - Theoretical Computer Science

JF - Theoretical Computer Science

ER -