2020

• 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

• Abdolhamid Ghodselahi, Fabian Kuhn, Volker Turau
  Competitive Concurrent Distributed Scheduling
  2019 30th Int. Symp. on Algorithms and Computation (ISAAC)

2017

• Abdolhamid Ghodselahi, Fabian Kuhn
  Dynamic Analysis of the Arrow Distributed Directory Protocol in General Networks
  2017 31st Symposium on Distributed Computing (DISC)
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  Abstract

  The Arrow protocol is a simple and elegant protocol to coordinate exclusive access to a shared object in a network. The protocol solves the underlying distributed queueing problem by using path reversal on a pre-computed spanning tree (or any other tree topology simulated on top of the given network). It is known that the Arrow protocol solves the problem with a competitive ratio of O(log D) on trees of diameter D. This implies a distributed queueing algorithm with competitive ratio O(s · log D) for general networks with a spanning tree of diameter D and stretch s. In this work we show that when running the Arrow protocol on top of the well-known probabilistic tree embedding of Fakcharoenphol, Rao, and Talwar [STOC03], we obtain a randomized distributed queueing algorithm with a competitive ratio of O(log n) even on general network topologies. The result holds even if the queueing requests occur in an arbitrarily dynamic and concurrent fashion and even if communication is asynchronous. From a technical point of view, the main of the paper shows that the competitive ratio of the Arrow protocol is constant on a special family of tree topologies, known as hierarchically well separated trees.

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 $T<n-k$.
• Abdolhamid Ghodselahi, Fabian Kuhn
  Serving Online Requests with Mobile Servers
  2015 26th Int. Symp. on Algorithms and Computation (ISAAC), Nagoya, Japan
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  Abstract

  We study an online problem in which mobile servers have to be moved in order to efficiently serve a set of online requests. More formally, there is a set of n nodes and a set of k mobile servers that are placed at some of the nodes. Each node can potentially host several servers and the servers can be moved between the nodes. There are requests 1,2, ... that are adversarially issued at nodes one at a time, where a request issued at time t needs to be served at all times t' ≥ t. The cost for serving the requests is a function of the number of servers and requests at the different nodes. The requirements on how to serve the requests are governed by two parameters ɑ ≥ 1 and β ≥ 0. An algorithm needs to guarantee that at all times, the total service cost remains within a multiplicative factor of ɑ and an additive term β of the current optimal service cost. We consider online algorithms for two different minimization objectives. We first consider the natural problem of minimizing the total number of server movements. We show that in this case for every k, the competitive ratio of every deterministic online algorithm needs to be at least Ω(n). Given this negative result, we then extend the minimization objective to also include the current service cost. We give almost tight bounds on the competitive ratio of the online problem where one needs to minimize the sum of the total number of movements and the current service cost. In particular, we show that at the cost of an additional additive term which is roughly linear in k, it is possible to achieve a multiplicative competitive ratio of 1+ε for every constant ε>0.