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**Published in:** LIPIcs, Volume 149, 30th International Symposium on Algorithms and Computation (ISAAC 2019)

This paper introduces a new resource allocation problem in distributed computing called distributed serving with mobile servers (DSMS). In DSMS, there are k identical mobile servers residing at the processors of a network. At arbitrary points of time, any subset of processors can invoke one or more requests. To serve a request, one of the servers must move to the processor that invoked the request. Resource allocation is performed in a distributed manner since only the processor that invoked the request initially knows about it. All processors cooperate by passing messages to achieve correct resource allocation. They do this with the goal to minimize the communication cost.
Routing servers in large-scale distributed systems requires a scalable location service. We introduce the distributed protocol Gnn that solves the DSMS problem on overlay trees. We prove that Gnn is starvation-free and correctly integrates locating the servers and synchronizing the concurrent access to servers despite asynchrony, even when the requests are invoked over time. Further, we analyze Gnn for "one-shot" executions, i.e., all requests are invoked simultaneously. We prove that when running Gnn on top of a special family of tree topologies - known as hierarchically well-separated trees (HSTs) - we obtain a randomized distributed protocol with an expected competitive ratio of O(log n) on general network topologies with n processors. From a technical point of view, our main result is that Gnn optimally solves the DSMS problem on HSTs for one-shot executions, even if communication is asynchronous. Further, we present a lower bound of Omega(max {k, log n/log log n}) on the competitive ratio for DSMS. The lower bound even holds when communication is synchronous and requests are invoked sequentially.

Abdolhamid Ghodselahi, Fabian Kuhn, and Volker Turau. Concurrent Distributed Serving with Mobile Servers. In 30th International Symposium on Algorithms and Computation (ISAAC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 149, pp. 53:1-53:18, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)

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@InProceedings{ghodselahi_et_al:LIPIcs.ISAAC.2019.53, author = {Ghodselahi, Abdolhamid and Kuhn, Fabian and Turau, Volker}, title = {{Concurrent Distributed Serving with Mobile Servers}}, booktitle = {30th International Symposium on Algorithms and Computation (ISAAC 2019)}, pages = {53:1--53:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-130-6}, ISSN = {1868-8969}, year = {2019}, volume = {149}, editor = {Lu, Pinyan and Zhang, Guochuan}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2019.53}, URN = {urn:nbn:de:0030-drops-115497}, doi = {10.4230/LIPIcs.ISAAC.2019.53}, annote = {Keywords: Distributed online resource allocation, Distributed directory, Asynchronous communication, Amortized analysis, Tree embeddings} }

Document

**Published in:** LIPIcs, Volume 91, 31st International Symposium on Distributed Computing (DISC 2017)

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 [STOC'03], we obtain a randomized distributed online queueing algorithm with expected competitive ratio O(log n) against an oblivious adversary even on general n-node network topologies. The result holds even if the queueing requests occur in an arbitrarily dynamic and concurrent fashion and even if communication is asynchronous. The main technical result 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.

Abdolhamid Ghodselahi and Fabian Kuhn. Dynamic Analysis of the Arrow Distributed Directory Protocol in General Networks. In 31st International Symposium on Distributed Computing (DISC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 91, pp. 22:1-22:16, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2017)

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@InProceedings{ghodselahi_et_al:LIPIcs.DISC.2017.22, author = {Ghodselahi, Abdolhamid and Kuhn, Fabian}, title = {{Dynamic Analysis of the Arrow Distributed Directory Protocol in General Networks}}, booktitle = {31st International Symposium on Distributed Computing (DISC 2017)}, pages = {22:1--22:16}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-053-8}, ISSN = {1868-8969}, year = {2017}, volume = {91}, editor = {Richa, Andr\'{e}a}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2017.22}, URN = {urn:nbn:de:0030-drops-79857}, doi = {10.4230/LIPIcs.DISC.2017.22}, annote = {Keywords: Arrow protocol, competitive analysis, distributed queueing, shared objects, tree embeddings} }

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**Published in:** LIPIcs, Volume 46, 19th International Conference on Principles of Distributed Systems (OPODIS 2015)

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 >= 1 and k => 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 >= 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 >= 1, any k >= 1, and any tau = 1, for a tau-oblivious adversary, there is a distributed algorithm to broadcast a single message in time O((1+n/(k * min(tau,T)) * n *log^3(n)). 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 <= (n/k)^{1-epsilon} (for any constant epsilon > 0) and for any k >= 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.

Mohamad Ahmadi, Abdolhamid Ghodselahi, Fabian Kuhn, and Anisur Rahaman Molla. The Cost of Global Broadcast in Dynamic Radio Networks. In 19th International Conference on Principles of Distributed Systems (OPODIS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 46, pp. 7:1-7:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{ahmadi_et_al:LIPIcs.OPODIS.2015.7, author = {Ahmadi, Mohamad and Ghodselahi, Abdolhamid and Kuhn, Fabian and Molla, Anisur Rahaman}, title = {{The Cost of Global Broadcast in Dynamic Radio Networks}}, booktitle = {19th International Conference on Principles of Distributed Systems (OPODIS 2015)}, pages = {7:1--7:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-98-9}, ISSN = {1868-8969}, year = {2016}, volume = {46}, editor = {Anceaume, Emmanuelle and Cachin, Christian and Potop-Butucaru, Maria}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2015.7}, URN = {urn:nbn:de:0030-drops-65989}, doi = {10.4230/LIPIcs.OPODIS.2015.7}, annote = {Keywords: radio network, dynamic network, global broadcast, interval connectivity, hitting game} }

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