Approximate Proof-Labeling Schemes

Censor-Hillel, Keren; Paz, Ami; Perry, Mor

doi:10.1007/978-3-319-72050-0_5

Cited by 9 publications

(8 citation statements)

References 25 publications

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“…The proof-size of a PLS is the maximal size of a label assigned in it. We note that the above directly implies that lower bounds can be carried over from Theorem 1.1 to lower bounds on the proof-size of distributed predicates, which generalizes several previous lower bounds for PLS [12,22].…”

Section: Impossibility Using Proof Labeling Schemessupporting

confidence: 67%

“…A PLS for |M CM | < k with logarithmic labels was presented in [12], using a duality theorem of Tutte and Berge.…”

Section: Impossibility Using Proof Labeling Schemesmentioning

confidence: 99%

“…The proof follows the lines of the previous proofs: By Corollary 5.3, it is enough to show a PLS for P and a PLS for ¬P , both of size O(log n). For this, we employ known schemes (see, e.g., [4,12,31]) for acyclicity, spanning tree, and for pointing to a desired vertex or subgraph, without reproving them. All schemes have proof size O(log n).…”

Section: Impossibility Using Proof Labeling Schemesmentioning

confidence: 99%

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Hardness of Distributed Optimization

Bacrach

Censor-Hillel

Dory

et al. 2019

Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing

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This paper studies lower bounds for fundamental optimization problems in the congest model. We show that solving problems exactly in this model can be a hard task, by providing Ω(n 2 ) lower bounds for cornerstone problems, such as minimum dominating set (MDS), Hamiltonian path, Steiner tree and max-cut. These are almost tight, since all of these problems can be solved optimally in O(n 2 ) rounds. Moreover, we show that even in bounded-degree graphs and even in simple graphs with maximum degree 5 and logarithmic diameter, it holds that various tasks, such as finding a maximum independent set (MaxIS) or a minimum vertex cover, are still difficult, requiring a near-tight number ofΩ(n) rounds.Furthermore, we show that in some cases even approximations are difficult, by providing añ Ω(n 2 ) lower bound for a (7/8 + )-approximation for MaxIS, and a nearly-linear lower bound for an O(log n)-approximation for the k-MDS problem for any constant k ≥ 2, as well as for several variants of the Steiner tree problem.Our lower bounds are based on a rich variety of constructions that leverage novel observations, and reductions among problems that are specialized for the congest model. However, for several additional approximation problems, as well as for exact computation of some central problems in P , such as maximum matching and max flow, we show that such constructions cannot be designed, by which we exemplify some limitations of this framework.Lower bounds for exact computation. We show that in many cases, solving problems exactly in the congest model is hard, by providing many newΩ(n 2 ) lower bounds for fundamental optimization problems, such as MDS, max-cut, Hamiltonian path, Steiner tree and minimum 2edge-connected spanning subgraph (2-ECSS). Such results were previously known only for the minimum vertex cover (MVC), MaxIS and minimum chromatic number problems [10]. Our results are inspired by [10], but combine many new technical ingredients. In particular, one of the key components in our lower bounds are reductions between problems. After having a lower bound for MDS, a cleverly designed reduction allows us to build a new lower bound construction for Hamiltonian path. These constructions serve as a basis for our constructions for the Steiner tree and minimum 2-ECSS. We emphasize that we cannot use directly known reductions from the sequential setting, but rather we must create reductions that can be applied efficiently on lower bound constructions.To demonstrate the challenge, we now give more details about the general framework. We use the well-known framework of reductions from 2-party communication complexity, as originated in [44] and used in many additional works, e.g., [1, 9,14,17,18,47]. In communication complexity, two players, Alice and Bob, receive private input strings and their goal is to solve some problem related to their inputs, for example, decide whether their inputs are disjoint, by communicating the minimum number of bits possible. To show a lower bound for the congest model, the highlevel idea is t...

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Section: Impossibility Using Proof Labeling Schemessupporting

confidence: 67%

“…A PLS for |M CM | < k with logarithmic labels was presented in [12], using a duality theorem of Tutte and Berge.…”

Section: Impossibility Using Proof Labeling Schemesmentioning

confidence: 99%

Section: Impossibility Using Proof Labeling Schemesmentioning

confidence: 99%

See 1 more Smart Citation

Hardness of Distributed Optimization

Bacrach

Censor-Hillel

Dory

et al. 2019

Proceedings of the 2019 ACM Symposium on Principles of Distributed Computing

Self Cite

View full text Add to dashboard Cite

show abstract

“…We understand our work as a first step, and believe that it opens several interesting avenues for future research. In particular, it will also be interesting to consider the use of randomized [21] and approximate [22] solutions to improve our approach, provide extensions to further consistency properties such as waypoints [23] and congestion [24], as well as seamless updates [25], but also the inherent connections to self-stabilization [26]. More generally, we believe that our approach can provide interesting new perspectives on emerging self-driving networks [27], which center around fine-grained and fast adaptions of networks reacting to their environment, and may hence benefit from our distributed approaches.…”

Section: Resultsmentioning

confidence: 99%

Distributed Consistent Network Updates in SDNs: Local Verification for Global Guarantees

Foerster

Schmid

2019

2019 IEEE 18th International Symposium on Network Computing and Applications (NCA)

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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 which the consistent network updates are implemented by the switches and routers directly in the data plane. In particular, our approach leverages concepts from local proof labeling systems, which allows the data plane elements to locally check network properties, and we show that this is sufficient to obtain global network guarantees. We demonstrate our approach considering three fundamental use cases, and analyze its benefits in terms of performance and fault-tolerance.

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“…An important result in the area is the tight bound on the size of the certificates for certifying minimum spanning tree [13]. Recently, several variations have been defined, for verifying approximation [3], with non-constant verification radius [20], with a dependency between the number of errors and the distance to the language [6], and variations on the communication model [22]. An analogue of the polynomial hierarchy for distributed decision has also been defined [7].…”

Section: Related Workmentioning

confidence: 99%

Local verification of global proofs

Feuilloley,

Hirvonen

2018

Preprint

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In this work we study the cost of local and global proofs on distributed verification. In this setting the nodes of a distributed system are provided with a nondeterministic proof for the correctness of the state of the system, and the nodes need to verify this proof by looking at only their local neighborhood in the system.Previous works have studied the model where each node is given its own, possibly unique, part of the proof as input. The cost of a proof is the maximum size of an individual label. We compare this model to a model where each node has access to the same global proof, and the cost is the size of this global proof.It is easy to see that a global proof can always include all of the local proofs, and every local proof can be a copy of the global proof. We show that there exists properties that exhibit these relative proof sizes, and also properties that are somewhere in between. In addition, we introduce a new lower bound technique and use it to prove a tight lower bound on the complexity of reversing distributed decision and establish a link between communication complexity and distributed proof complexity.

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Approximate Proof-Labeling Schemes

Cited by 9 publications

References 25 publications

Hardness of Distributed Optimization

Hardness of Distributed Optimization

Distributed Consistent Network Updates in SDNs: Local Verification for Global Guarantees

Local verification of global proofs

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