2018

• Mohamad Ahmadi, Fabian Kuhn, Rotem Oshman
  Distributed Approximate Maximum Matching in the CONGEST Model
  2018 32th Int. Symp. on Distributed Computing (DISC), New Orleans, USA
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  Abstract

  We study distributed algorithms for the maximum matching problem in the CONGEST model, where each message must be bounded in size. We give new deterministic upper bounds, and a new lower bound on the problem. We begin by giving a distributed algorithm that computes an exact maximum (unweighted) matching in bipartite graphs, in O(n log n) rounds. Next, we give a distributed algorithm that approximates the fractional weighted maximum matching problem in general graphs. In a graph with maximum degree at most Delta, the algorithm computes a (1-eps)-approximation for the problem in time O(log(Delta W)/eps^2), where W is a bound on the ratio between the largest and the smallest edge weight. Next, we show a slightly improved and generalized version of the deterministic rounding algorithm of Fischer [DISC '17]. Given a fractional weighted maximum matching solution of value f for a given graph G, we show that in time O((log^2(Delta)+log^*n)/eps), the fractional solution can be turned into an integer solution of value at least (1-eps)f for bipartite graphs and (1-\eps).f.(g-1)/g for general graphs, where g is the length of the shortest odd cycle of G. Together with the above fractional maximum matching algorithm, this implies a deterministic algorithm that computes a (1-eps).f.(g-1)/g-approximation for the weighted maximum matching problem in time O(log(Delta W)/eps^2 + (log^2(Delta)+log^* n)/eps). On the lower-bound front, we show that even for unweighted fractional maximum matching in bipartite graphs, computing an (1 - O(1/sqrt{n}))-approximate solution requires at least Omega(D+sqrt{n}) rounds in CONGEST (ignoring log factors). This lower bound requires the introduction of a new 2-party communication problem, for which we prove a tight lower bound.

2016

• Mohamad Ahmadi, Fabian Kuhn
  Multi-Message Broadcast in Dynamic Radio Networks
  2016 12th Int. Symp. on Algorithms and Experiments for Wireless Sensor Networks (ALGOSENSORS), Aarhus, Denmark
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  Abstract

  We continue the recent line of research studying information dissemination problems in adversarial dynamic radio networks. We give two generic algorithms which allow to transform generalized version of single-message broadcast algorithms into multi-message broadcast algorithms. Based on these generic algorithms, we obtain multi-message broadcast algorithms for dynamic radio networks for a number of different dynamic network settings. For one of the modeling assumptions, our algorithms are complemented by a lower bound which shows that the upper bound is close to optimal.

2015

• Mohamad Ahmadi, Abdolhamid Ghodselahi, Fabian Kuhn, Anisur Rahaman Molla
  The Cost of Global Broadcast in Dynamic Radio Networks
  2015 19th Int. Conf. on Principles of Distributed Systems (OPODIS), Rennes, France
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  Abstract

  We study the single-message broadcast problem in dynamic radio networks. We show that the time complexity of the problem depends on the amount of stability and connectivity of the dynamic network topology and on the adaptiveness of the adversary providing the dynamic topology. More formally, we model communication using the standard graph-based radio network model. To model the dynamic network, we use a variant of the synchronous dynamic graph model introduced in [Kuhn et al., STOC 2010]. For integer parameters $T\geq 1$ and $k\geq 1$, we call a dynamic graph $T$-interval $k$-connected if for every interval of $T$ consecutive rounds, there exists a $k$-vertex-connected stable subgraph. Further, for an integer parameter $\tau\geq 0$, we say that the adversary providing the dynamic network is $\tau$-oblivious if for constructing the graph of some round $t$, the adversary has access to all the randomness (and states) of the algorithm up to round $t-\tau$. As our main result, we show that for any $T\geq 1$, any $k\geq 1$, and any $\tau\geq 1$, for a $\tau$-oblivious adversary, there is a distributed algorithm to broadcast a single message in time $O\big(\big(1+\frac{n}{k\cdot \min \set{\tau,T}} \big ) \cdot n \log^3 n \big)$. We further show that even for large interval $k$-connectivity, efficient broadcast is not possible for the usual adaptive adversaries. For a $1$-oblivious adversary, we show that even for any $T\leq (n/k)^{1-\eps}$ (for any constant $\eps > 0$) and for any $k\geq 1$, global broadcast in $T$-interval $k$-connected networks requires at least $\Omega(n^2/k^2\log n)$ time. Further, for a $0$-oblivious adversary, broadcast cannot be solved in $T$-interval $k$-connected networks as long as $T<n-k$.