DeepAI

# Computing Power of Hybrid Models in Synchronous Networks

During the last two decades, a small set of distributed computing models for networks have emerged, among which LOCAL, CONGEST, and Broadcast Congested Clique (BCC) play a prominent role. We consider hybrid models resulting from combining these three models. That is, we analyze the computing power of models allowing to, say, perform a constant number of rounds of CONGEST, then a constant number of rounds of LOCAL, then a constant number of rounds of BCC, possibly repeating this figure a constant number of times. We specifically focus on 2-round models, and we establish the complete picture of the relative powers of these models. That is, for every pair of such models, we determine whether one is (strictly) stronger than the other, or whether the two models are incomparable. The separation results are obtained by approaching communication complexity through an original angle, which may be of independent interest. The two players are not bounded to compute the value of a binary function, but the combined outputs of the two players are constrained by this value. In particular, we introduce the XOR-Index problem, in which Alice is given a binary vector x∈{0,1}^n together with an index i∈[n], Bob is given a binary vector y∈{0,1}^n together with an index j∈[n], and, after a single round of 2-way communication, Alice must output a boolean out_A, and Bob must output a boolean out_B, such that _A_B = x_j⊕ y_i. We show that the communication complexity of XOR-Index is Ω(n) bits.

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09/19/2022

### Rounds vs Communication Tradeoffs for Maximal Independent Sets

We consider the problem of finding a maximal independent set (MIS) in th...
07/23/2018

### Random Sampling Applied to the MST Problem in the Node Congested Clique Model

The Congested Clique model, proposed by Lotker et al. [SPAA'03, SICOMP'0...
11/05/2018

### The distributed complexity of locally checkable problems on paths is decidable

Consider a computer network that consists of a path with n nodes. The no...
12/09/2019

### A Deterministic Algorithm for the MST Problem in Constant Rounds of Congested Clique

In this paper, we show that the Minimum Spanning Tree problem can be sol...
09/18/2019

### Message Reduction in the Local Model is a Free Lunch

A new spanner construction algorithm is presented, working under the LOC...
08/23/2022

### Strong XOR Lemma for Communication with Bounded Rounds

In this paper, we prove a strong XOR lemma for bounded-round two-player ...
05/16/2023

### A Local Perspective on the Polynomial Hierarchy

We extend classical methods of computational complexity to the setting o...