
Distributed Lower Bounds for Ruling Sets
Given a graph G = (V,E), an (α, β)ruling set is a subset S ⊆ V such tha...
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Truly TightinΔ Bounds for Bipartite Maximal Matching and Variants
In a recent breakthrough result, Balliu et al. [FOCS'19] proved a determ...
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Local Problems on Trees from the Perspectives of Distributed Algorithms, Finitary Factors, and Descriptive Combinatorics
We study connections between distributed local algorithms, finitary fact...
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A Breezing Proof of the KMW Bound
In their seminal paper from 2004, Kuhn, Moscibroda, and Wattenhofer (KMW...
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A Simple Proof of a New Set Disjointness with Applications to Data Streams
The multiplayer promise set disjointness is one of the most widely used ...
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Distributed Reconfiguration of Maximal Independent Sets
Consider the following problem: given a graph and two maximal independen...
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Distributed Graph Realizations
We study graph realization problems from a distributed perspective and w...
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Improved Distributed Lower Bounds for MIS and Bounded (Out)Degree Dominating Sets in Trees
Recently, Balliu, Brandt, and Olivetti [FOCS '20] showed the first ω(log^* n) lower bound for the maximal independent set (MIS) problem in trees. In this work we prove lower bounds for a much more relaxed family of distributed symmetry breaking problems. As a byproduct, we obtain improved lower bounds for the distributed MIS problem in trees. For a parameter k and an orientation of the edges of a graph G, we say that a subset S of the nodes of G is a koutdegree dominating set if S is a dominating set of G and if in the induced subgraph G[S], every node in S has outdegree at most k. Note that for k=0, this definition coincides with the definition of an MIS. For a given k, we consider the problem of computing a koutdegree dominating set. We show that, even in regular trees of degree at most Δ, in the standard model, there exists a constant ϵ>0 such that for k≤Δ^ϵ, for the problem of computing a koutdegree dominating set, any randomized algorithm requires at least Ω(min{logΔ,√(loglog n)}) rounds and any deterministic algorithm requires at least Ω(min{logΔ,√(log n)}) rounds. The proof of our lower bounds is based on the recently highly successful round elimination technique. We provide a novel way to do simplifications for round elimination, which we expect to be of independent interest. Our new proof is considerably simpler than the lower bound proof in [FOCS '20]. In particular, our round elimination proof uses a family of problems that can be described by only a constant number of labels. The existence of such a proof for the MIS problem was believed impossible by the authors of [FOCS '20].
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