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Beyond geometry : Towards fully realistic wireless models
(Association for Computing Machinery, 2014-07-15) Bodlaender, Marijke H.L.; Halldórsson, Magnús M.
Signal-strength models of wireless communications capture the gradual fading of signals and the additivity of interference. As such, they are closer to reality than other models. However, nearly all theoretic work in the SINR model depends on the assumption of smooth geometric decay, one that is true in free space but is far off in actual environments. The challenge is to model realistic environments, including walls, obstacles, reflections and anisotropic antennas, without making the models algorithmically impractical or analytically intractable. We present a simple solution that allows the modeling of arbitrary static situations by moving from geometry to arbitrary decay spaces. The complexity of a setting is captured by a metricity parameter ζ that indicates how far the decay space is from satisfying the triangular inequality. All results that hold in the SINR model in general metrics carry over to decay spaces, with the resulting time complexity and approximation depending on ζ in the same way that the original results depends on the path loss term α. For distributed algorithms, that to date have appeared to necessarily depend on the planarity, we indicate how they can be adapted to arbitrary decay spaces at a cost in time complexity that depends on a fading parameter of the decay space. In particular, for decay spaces that are doubling, the parameter is constant-bounded. Finally, we explore the dependence on ζ in the approximability of core problems. In particular, we observe that the capacity maximization problem has exponential upper and lower bounds in terms of ζ in general decay spaces. In Euclidean metrics and related growth-bounded decay spaces, the performance depends on the exact metricity definition, with a polynomial upper bound in terms of ζ but an exponential lower bound in terms of a variant parameter φ. The upper bound result is the first approximation of a capacity-type SINR problem that is subexponential in α.
Verk
Connectivity and aggregation in multihop wireless networks
(Association for Computing Machinery, 2013-07-22) Bodlaender, Marijke H.L.; Halldórsson, Magnús M.; Mitra, Pradipta; Department of Computer Science
We present randomized distributed algorithms for connectivity and aggregation in multi-hop wireless networks under the SINR model. The connectivity problem asks for a set of links that strongly connect a given set of wireless nodes, along with an efficient schedule. Aggregation asks for a spanning in-arborescence (converge-cast tree), along with a schedule that additionally obeys the partial order defined by the tree. Here we treat the multi-hop case, where nodes have limited power that restricts the links they can potentially form. We show that connectivity is possible for any set of n nodes in O(log n) slots, which matches the best centralized bound known, and that aggregation is possible in O(D +log n) time (D being the maximum hop-distance), which is optimal.
Verk
Online set packing and competitive scheduling of multi-part tasks
(Association for Computing Machinery (ACM), 2010-07-25) Emek, Yuval; Halldórsson, Magnús M.; Mansour, Yishay; Patt-Shamir, Boaz; Radhakrishnan, Jaikumar; Rawitz, Dror; Department of Computer Science
We consider a scenario where large data frames are broken into a few packets and transmitted over the network. Our focus is on a bottleneck router: the model assumes that in each time step, a set of packets (a burst) arrives, from which only one packet can be served, and all other packets are lost. A data frame is considered useful only if none of its constituent packets is lost, and otherwise it is worthless. We abstract the problem as a new type of online set packing, present a randomized distributed algorithm and a matching lower bound on the competitive ratio for any randomized online algorithm. Our bounds are expressed in terms of the maximal burst size and the maximal number of packets per frame. We also present refined bounds that depend on the uniformity of these parameters.
Verk
Prevalence of autism in an urban population of adults with severe intellectual disabilities - a preliminary study
(2010) Saemundsen, E.; Juliusson, H.; Hjaltested, S.; Gunnarsdottir, T.; Halldorsdottir, T.; Hreidarsson, S.; Magnusson, P.
Verk
On spectrum sharing games
(Association for Computing Machinery, 2004-07-25) Halldórsson, Magnús M.; Li, Li; Halpern, Joseph Y.; Mirrokni, Vahab S.; Department of Computer Science
Each access point (AP) in a WiFi network must be assigned a channel for it to service users. There are only finitely many possible channels that can be assigned. Moreover, neighboring access points must use different channels so as to avoid interference. Currently these channels are assigned by administrators who carefully consider channel conflicts and network loads. Channel conflicts among APs operated by different entities are currently resolved in an ad hoc manner or not resolved at all. We view the channel assignment problem as a game, where the players are the service providers and APs are acquired sequentially. We consider the price of anarchy of this game, which is the ratio between the total coverage of the APs in the worst Nash equilibrium of the game and what the total coverage of the APs would be if the channel assignment were done by a central authority. We provide bounds on the price of anarchy depending on assumptions on the underlying network and the type of bargaining allowed between service providers. The key tool in the analysis is the identification of the Nash equilibria with the solutions to a maximal coloring problem in an appropriate graph. We relate the price of anarchy of these games to the approximation factor of local optimization algorithms for the maximum k-colorable subgraph problem. We also study the speed of convergence in these games.

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