2020

• Mohamad Ahmadi, Fabian Kuhn
  Distributed Maximum Matching Verification in CONGEST
  2020 34rd International Symposium on Distributed Computing (DISC)
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  Abstract

  We study the maximum cardinality matching problem in a standard distributed setting, where the nodes V of a given n-node network graph G = (V,E) communicate over the edges E in synchronous rounds. More specifically, we consider the distributed CONGEST model, where in each round, each node of G can send an O(log n)-bit message to each of its neighbors. We show that for every graph G and a matching M of G, there is a randomized CONGEST algorithm to verify M being a maximum matching of G in time O(|M|) and disprove it in time O(D + ), where D is the diameter of G and is the length of a shortest augmenting path. We hope that our algorithm constitutes a significant step towards developing a CONGEST algorithm to compute a maximum matching in time Õ(s^*), where s^* is the size of a maximum matching.

• Mohamad Ahmadi, Abdolhamid Ghodselahi, Fabian Kuhn, Anisur Rahaman Molla
  The Cost of Global Broadcast in Dynamic Radio Networks
  2020 Theor Comput Sci, volume: 806, pages: 363 - 387
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  Abstract

  We study the time complexity of single and multi token broadcast in adversarial dynamic radio networks. Initially, k tokens (which are k pieces of information) are distributed among the n nodes of a network and all the tokens need to be disseminated to all the nodes in the network. We first consider the single-token broadcast problem (i.e., the case k=1). By presenting upper and lower bounds, we show that the time complexity of single-token broadcast depends on the amount of stability and connectivity of the dynamic network topology and on the adaptiveness of the adversary providing the dynamic topology. Then, we give two generic algorithms which allow to transform generalized forms of single-token broadcast algorithms into multi-token broadcast (k-token broadcast) algorithms. Based on these generic algorithms, we obtain k-token broadcast algorithms for a number of different dynamic network settings. For one of the modeling assumptions, our algorithm is complemented by a lower bound which shows that the upper bound is close to optimal.

2019

• Mohamad Ahmadi, Fabian Kuhn, Shay Kutten, Anisur Rahaman Molla, Gopal Pandurangan
  The Communication Cost of Information Spreading in Dynamic Networks
  2019 39th IEEE Int. Conf. on Distributed Computing Systems (ICDCS), Dallas, USA
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  Abstract

  This paper investigates the message complexity of distributed information spreading in adversarial dynamic net- works. While distributed computations in dynamic networks have been studied intensively over the last years, almost all of the existing work solely focuses on the time complexity of distributed algorithms. In information spreading, the goal is to spread k tokens of information to every node on an n-node network. We consider the amortized (average) message complexity of spreading a token, assuming that the number of tokens is large. In a static network, this basic problem can be solved using (asymptotically optimal) O(n) amortized messages per token. Our focus is on token-forwarding algorithms, which do not manipulate tokens in any way other than storing, copying, and forwarding them. We present two sets of results depending on how nodes send messages to their neighbors: 1. Local broadcast: We show a tight lower bound of \tilde{Ω}(n^2) on the number of amortized local broadcasts, which is matched by the naive flooding algorithm. The lower bound holds for randomized algorithms against a strongly adaptive adversary. 2. Unicast: We study the message complexity as a function of the number of dynamic changes in the network. To facilitate this, we introduce adversary-competitive message complexity as a natural complexity measure for analyzing dynamic networks: The adversary pays a unit cost for every topological change and the message cost of an algorithm is determined as the actual number of messages sent minus the total cost of the adversary. Under this model, we give a deterministic algorithm that obtains an optimal amortized message complexity of O(n) if the number of tokens k is sufficiently large. We also present a randomized algorithm that achieves subquadratic amortized message complexity for much smaller k under an oblivious adversary.

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 $T<n-k$.