*Serving Online Requests with Mobile Resources*. PhD Thesis, University of Freiburg, Freiburg, Germany, 2018.

# Abdolhamid Ghodselahi

## Forschungsinteressen

Ich bin generell an kombinatorischen Optimierungs- und Approximationsalgorithmen interessiert. Insbesondere studiere ich hauptsächlich Probleme, die sowohl in verteilten als auch in zentralisierten Systemen online auftreten können. Ich bin daran interessiert, Online-Algorithmen für solche Probleme zu entwerfen und zu analysieren, insbesondere Online-Zuweisungsprobleme.

## kurzer Lebenslauf

Ich bin Postdoc-Forscher an der Technische Universität Hamburg und arbeite seit August 2018 mit Prof. Dr. Volker Turau . Ich war Doktorand an der Universität Freiburg unter der Leitung von Prof. Dr. Fabian Kuhn . Ich habe einen M.Sc. in Algorithmen und Berechnung von der Universität Teheran. Mein Vorgesetzter war Prof. Dr. Mohammad Ali Safari .

## Projekte

- ToleranceZone - Fehlertolerante Middleware-Idiome basierend auf selbststabilisierenden Techniken

## Publikationen

**Abstract**: Resource allocation problems have a large variety of applications in different areas of computer science and operations research. A resource allocation problem seeks to find an optimal allocation of a given type of expensive or limited resource to a set of clients that request the services of the given resource. Some of these problems have an online nature: The requests sequence is not revealed at the beginning, but the requests arrive in an online fashion. An algorithm for an online resource allocation problem must make its decision in response to a newly arriving request in an online fashion, i.e., typically before the subsequent request arrives. Depending on the definition of an online resource allocation problem, it might be allowed to postpone serving a request or to change an already made decision. However in this case, postponing a service and changing a decision come at a cost. In this thesis, we also study online allocation problems in the distributed setting, where in contrast to a centralized system, there is no central unit that controls everything and that is aware of the global state of the system. In addition to the uncertainty about the request sequence arising from the online arrivals, there is also uncertainty at each node in the network because the node does not directly learn about requests arriving in other parts of the network. The nodes of a distributed system therefore need to communicate in order to coordinate their actions and one typically assumes that this communication does not come for free. Two online problems are mainly studied in this thesis. First, we consider the distributed queuing problem as a basic problem that coordinates mutually exclusive access to shared data in distributed systems. We devise a randomized distributed queuing algorithm with an expected competitive ratio of O(log n) on general network topologies. We utilize the well-known probabilistic tree embedding of Fakcharoenphol, Rao, and Talwar [STOC 2003] that approximates the distances of a general metric space by mapping it to a special family of tree topologies known as hierarchically well-separated trees and often just referred to as HSTs. Our randomized distributed queuing algorithm is obtained by running the ARROW algorithm—a well-known distributed queuing algorithm—on top of the HST that is produced by applying the above embedding to the distances of the underlying network. It is shown that (under some assumptions) the simple and elegant ARROW algorithm outperforms all existing significantly more complicated distributed queueing algorithms. The second main problem that is studied in a centralized setting is the online facility location problem. We introduce the online mobile facility location (OMFL) problem, where the facilities are mobile. A lower bound for the OMFL problem that even holds on uniform metrics is provided. A natural approach to solve the OMFL problem for general metric spaces is to again use the above embedding into an HST and to directly solve the OMFL problem on HSTs. In this thesis, we provide a first step in this direction by solving a generalized version of the OMFL problem on uniform metrics. A simple deterministic online algorithm is devised and a tight analysis is provided for the algorithm. The second step remains as an open question. We further introduce and study another variant of the OMFL problem that is closer to the k-server problem, arguably one of the most influential problem in the area of online algorithms and competitive analysis.

*Proceedings of the 31st International Symposium on Distributed Computing (DISC 2017)*, Oktober 2017, pp. 1–22. Vienna, Austria.

**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 [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.

*Proceedings of the 19th International Conference on Principles of Distributed Systems (OPODIS 2015)*, Dezember 2015, pp. 1–17. Rennes, France.

**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 ≥ 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 τ ≥ 0, we say that the adversary providing the dynamic network is τ-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-τ. As our main result, we show that for any T ≥ 1, any k ≥ 1, and any τ ≥ 1, for a τ-oblivious adversary, there is a distributed algorithm to broadcast a single message in time O((1+n/(k · min{τ,T})) · n log³n ). 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-ε) (for any constant ε > 0) and for any k ≥ 1, global broadcast in T-interval k-connected networks requires at least Ω(n²/k² 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.

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