Papers by Magnus M. Halldorsson
Dlt, 2010
A graph G = (V, E) is representable if there exists a word W over the alphabet V such that letter... more A graph G = (V, E) is representable if there exists a word W over the alphabet V such that letters x and y alternate in W if and only if (x, y) ∈ E for each x = y. If W is k-uniform (each letter of W occurs exactly k times in it) then G is called k-representable. A graph is representable if and only if it is k-representable for some k .
Measurement Based Interference Models for Wireless Scheduling Algorithms
ABSTRACT Modeling physical layer behavior of packet reception in the presence of interference is ... more ABSTRACT Modeling physical layer behavior of packet reception in the presence of interference is central to achieving efficient spectrum use in wireless sensor networks via spatial reuse. On one hand, analytic and simulations research has largely relied on assumptions of geometric path loss and isotropic transmission which have not been borne out in experiments. Experimental research, on the other hand, has not adopted theoretical models and instead focused on measuring the reality on the ground. We propose a new framework for wireless algorithms. First, distance-based path loss is replaced by an arbitrary gain matrix, typically obtained by measurements of received signal strength (RSS). This allows for the modeling of complex environments, e.g., with obstacles and walls. Second, a new parameter $\zeta$ indicates how close the gain matrix is to a distance metric, effectively measuring the complexity of the environment. We experimentally validate our framework on two indoors testbeds with 20 and 60 motes. The results validate the basic properties of the model, the predictive ability of packet reception, dominance over distance-based models, and the sensitivity of $\zeta$ to the nature of the environment. Theoretically, we show that \emph{all} known SINR scheduling algorithms that work in general metric spaces carry over and achieve equivalent performance guarantees in the new model. The conclusions suggest that wireless theory can finally be grounded in experimental practice.
Extending wireless algorithm design to arbitrary environments via metricity
Proceedings of the 17th Acm International Conference, Sep 21, 2014
Automata, Languages and Programming, 35th International Colloquium, ICALP 2008, Reykjavik, Iceland, July 7-11, 2008, Proceedings, Part II - Track B: Logic, Semantics, and Theory of Programming & Track C: Security and Cryptography Foundations
Icalp, 2008
The Wageningen UR Library Catalogue contains bibliographic data on books and periodicals held by ... more The Wageningen UR Library Catalogue contains bibliographic data on books and periodicals held by the libraries of Wageningen University and Research Centre and some 15 associated libraries. Holding data are added to each record. ... Subjects covered include Agrotechnology, Food and Food Production, Plant and Animal Sciences, Soil Science, Geo-information, Landscape and Spatial Planning, Water and Climate, Ecosystem Studies, Economics and Society. ... The joint collections of the participating libraries cover a substantial part of ...
At the heart of our approach is a new parameter $\zeta$ called metricity which indicates how clos... more At the heart of our approach is a new parameter $\zeta$ called metricity which indicates how close the gain matrix is to a distance metric, effectively measuring the complexity of the environment. A powerful theoretical feature of this parameter is that all known SINR scheduling algorithms that work in general metric spaces carry over to arbitrary gain matrices and achieve equivalent performance guarantees in terms of $\zeta$ as previously obtained in terms of the path loss constant. Our experiments confirm the sensitivity of $\zeta$ to the nature of the environment. Finally, we show analytically and empirically how multiple channels can be leveraged to improve metricity and thereby performance. We believe our contributions will facilitate experimental validation for recent advances in algorithms for physical wireless interference models.
We give algorithms with constant-factor performance guarantees for several capacity and throughpu... more We give algorithms with constant-factor performance guarantees for several capacity and throughput problems in the SINR model. The algorithms are all based on a novel LP formulation for capacity problems. First, we give a new constant-factor approximation algorithm for selecting the maximum subset of links that can be scheduled simultaneously, under any non-decreasing and sublinear power assignment. For the case of uniform power, we extend this to the case of variable QoS requirements and link-dependent noise terms. Second, we approximate a problem related to cognitive radio: find a maximum set of links that can be simultaneously scheduled without affecting a given set of previously assigned links. Finally, we obtain constant-factor approximation of weighted capacity under linear power assignment.
Acm Transactions on Algorithms, Dec 1, 2012
We consider the scheduling of arbitrary wireless links in the physical model of interference to m... more We consider the scheduling of arbitrary wireless links in the physical model of interference to minimize the time for satisfying all requests. We study here the combined problem of scheduling and power control, where we seek both an assignment of power settings and a partition of the links so that each set satisfies the signal-to-interference-plus-noise (SINR) constraints.
Efficient use of a wireless network requires that transmissions be grouped into feasible sets, wh... more Efficient use of a wireless network requires that transmissions be grouped into feasible sets, where feasibility means that each transmission can be successfully decoded in spite of the interference caused by simultaneous transmissions. Feasibility is most closely modeled by a signal-to-interference-plus-noise (SINR) formula, which unfortunately is conceptually complicated, being an asymmetric, cumulative, many-to-one relationship. We re-examine how well graphs can capture wireless receptions as encoded in SINR relationships, placing them in a framework in order to understand the limits of such modelling. We seek for each wireless instance a pair of graphs that provide upper and lower bounds on the feasibility relation, while aiming to minimize the gap between the two graphs. The cost of a graph formulation is the worst gap over all instances, and the price of (graph) abstraction is the smallest cost of a graph formulation. We propose a family of conflict graphs that is parameterized by a non-decreasing sub-linear function, and show that with a judicious choice of functions, the graphs can capture feasibility with a cost of $O(\log^* \Delta)$, where $\Delta$ is the ratio between the longest and the shortest link length. This holds on the plane and more generally in doubling metrics. We use this to give greatly improved $O(\log^* \Delta)$-approximation for fundamental link scheduling problems with arbitrary power control. We explore the limits of graph representations and find that our upper bound is tight: the price of graph abstraction is $\Omega(\log^* \Delta)$. We also give strong impossibility results for general metrics, and for approximations in terms of the number of links.
Minimizing Average Completion of Dedicated Tasks and Partially Ordered Sets
Scheduling dependent jobs on multiple machines is modeled as a graph (multi) coloring problem. Th... more Scheduling dependent jobs on multiple machines is modeled as a graph (multi) coloring problem. The focus of this work is on the sum of completion times measure. This is known as the sum (multi) coloring of the conflict graph. We also initiate the study of the waiting time and the robust throughput of colorings. For uniform-length tasks we give an algorithm which simultaneously approximates these two measures, as well as sum coloring and the chromatic number, within constant factor, for any graph in which the k-colorable subgraph ...
Multicoloring Planar Graphs and Partial k-Trees
We study the multicoloring problem with two objective functions: minimizing the makespan and mini... more We study the multicoloring problem with two objective functions: minimizing the makespan and minimizing the multisum. We focus on partial k-trees and planar graphs. In particular, we give polynomial time approximation schemes (PTAS) for both classes, for both preemptive and non-preemptive multisum colorings.
A graph $G=(V,E)$ is representable if there exists a word $W$ over the alphabet $V$ such that let... more A graph $G=(V,E)$ is representable if there exists a word $W$ over the alphabet $V$ such that letters $x$ and $y$ alternate in $W$ if and only if $(x,y)\in E$ for each $x\neq y$. If $W$ is $k$-uniform (each letter of $W$ occurs exactly $k$ times in it) then $G$ is called $k$-representable. It was shown that a graph is
We prove optimal bounds for inductive independence, implying a number of algorithmic applications... more We prove optimal bounds for inductive independence, implying a number of algorithmic applications. An algorithm is provided that achieves --- due to existing lower bounds --- capacity that is asymptotically best possible using oblivious power assignments. Improved approximation algorithms are provided for a number of problems for oblivious power and for power control, including distributed scheduling, connectivity, secondary spectrum auctions, and dynamic packet scheduling.
Proceedings of the 2015 ACM Symposium on Principles of Distributed Computing - PODC '15, 2015
We present the first algorithm that implements an abstract MAC (absMAC) layer in the Signal-to-In... more We present the first algorithm that implements an abstract MAC (absMAC) layer in the Signal-to-Interference-plus-Noise-Ratio (SINR) wireless network model. We first prove that efficient SINR implementations are not possible for the standard absMAC specification. We modify that specification to an "approximate" version that better suits the SINR model. We give an efficient algorithm to implement the modified specification, and use it to derive efficient algorithms for higher-level problems of global broadcast and consensus.
Proceedings of the Twenty Second Annual Acm Siam Symposium, Jan 23, 2011
We use this to give essentially tight characterizations of capacity maximization under power cont... more We use this to give essentially tight characterizations of capacity maximization under power control using oblivious power assignments. Specifically, we show that the mean power assignment is optimal for capacity maximization of bi-directional links, and give a tight $\theta(\log n)$-approximation of scheduling bi-directional links with power control using oblivious power. For uni-directional links we give a nearly optimal $O(\log n + \log \log \Delta)$-approximation to the power control problem using mean power, where $\Delta$ is the ratio of longest and shortest links. Combined, these results clarify significantly the centralized complexity of wireless communication problems.
Approximation Algorithms for the Maximum Power Consumption Problem on Combinatorial Circuits
Lecture Notes in Computer Science, 2000
The maximum power consumption problem on combinatorial circuits is the problem of estimating the ... more The maximum power consumption problem on combinatorial circuits is the problem of estimating the maximum power consumption of a given combinatorial circuit. It is easy to see that this problem for general circuits is hard to approximate within a factor of m I-∈, where m is the number of gates in an input circuit and∈ is any positive (small) constant. In this paper, we consider restricted circuits, namely, those consisting of only one level of AND/OR gates. Then the problem becomes a kind of MAX 2SAT where each variable takes one of four ...
Report on Two events at ICE-TCS, Reykjavik University
We first show that the known algorithms fail to obtain sub-logarithmic bounds; that is, their app... more We first show that the known algorithms fail to obtain sub-logarithmic bounds; that is, their approximation ratio are $\tilde\Omega(\log \max(\Delta,n))$, where $n$ is the number of links, $\Delta$ is the ratio of the maximum and minimum link lengths, and $\tilde\Omega$ hides doubly-logarithmic factors. We then present the first $O(\log{\log\Delta})$-approximation algorithm, which is known to be best possible (in terms of $\Delta$) for oblivious power schemes. We achieve this by representing interference by a conflict graph, which allows the application of graph-theoretic results for a variety of related problems, including the weighted capacity problem. We explore further the contours of approximability, and find the choice of power assignment matters; that not all metric spaces are equal; and that the presence of weak links makes the problem harder. Combined, our result resolve the price of oblivious power for wireless scheduling, or the value of allowing unfettered power control.
Coloring Powers of Planar Graphs (Algorithm Engineering as a New Paradigm)
数理解析研究所講究録, Dec 1, 1999
Greedy local improvement and weighted set packing approximation
Journal of Algorithms, May 1, 2001
Abstract Given a collection of weighted sets, each containing at most k elements drawn from a fin... more Abstract Given a collection of weighted sets, each containing at most k elements drawn from a finite base set, the kset packing problem is to find a maximum weight subcollection of disjoint sets. A greedy algorithm for this problem approximates it to within a factor of k, and natural local search has been shown to approximate it to within a factor of roughly k-1. However, neither paradigm can yield approximations that improve on this.
On some communication complexity problems related to threshold functions
Lecture Notes in Computer Science, 1993
We study the computation of threshold functions using formulas over the basis {AND, OR, NOT}, wit... more We study the computation of threshold functions using formulas over the basis {AND, OR, NOT}, with the aim of unifying the lower bounds of Hansel, Krichevskii, and Khrapchenko. For this we consider communication complexity problems related to threshold function computation.
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Papers by Magnus M. Halldorsson