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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.
Verk
Lower bounds for on-line graph coloring
(1994-08-01) Halldórsson, Magnus M.; Szegedy, Mario; Department of Computer Science
An algorithm for vertex-coloring graphs is said to be on-line if each vertex is irrevocably assigned a color before later vertices are considered. We show that for every such algorithm there exists a log n-colorable graph for which the algorithm uses at least 2n/log n colors. This also holds for randomized algorithms, to within a constant factor, against an oblivious adversary. We then show that various means of relaxing the constraints of the on-line model do not reduce these lower bounds. The features include presenting the input in blocks of up to log2 n vertices, recoloring any fraction of the vertices, presorting vertices by degree, and disclosing the adversary's previous coloring.

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