Conference Paper

# Brief announcement: distributed contention resolution in wireless networks.

DOI: 10.1145/1835698.1835731 Conference: Proceedings of the 29th Annual ACM Symposium on Principles of Distributed Computing, PODC 2010, Zurich, Switzerland, July 25-28, 2010

Source: DBLP

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**ABSTRACT:**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. We give an algorithm that attains an approximation ratio of $O(\log n \cdot \log\log \Delta)$, where $n$ is the number of links and $\Delta$ is the ratio between the longest and the shortest link length. Under the natural assumption that lengths are represented in binary, this gives the first approximation ratio that is polylogarithmic in the size of the input. The algorithm has the desirable property of using an oblivious power assignment, where the power assigned to a sender depends only on the length of the link. We give evidence that this dependence on $\Delta$ is unavoidable, showing that any reasonably-behaving oblivious power assignment results in a $\Omega(\log\log \Delta)$-approximation. These results hold also for the (weighted) capacity problem of finding a maximum (weighted) subset of links that can be scheduled in a single time slot. In addition, we obtain improved approximation for a bidirectional variant of the scheduling problem, give partial answers to questions about the utility of graphs for modeling physical interference, and generalize the setting from the standard 2-dimensional Euclidean plane to doubling metrics. Finally, we explore the utility of graph models in capturing wireless interference.Computing Research Repository - CORR. 10/2010; - [Show abstract] [Hide abstract]

**ABSTRACT:**To date, topology control in wireless ad hoc and sensor networks|the study of how to compute from the given com- munication network a subgraph with certain benecial prop- erties|has been considered as a static problem only; the time required to actually schedule the links of a computed topology without message collision was generally ignored. In this paper we analyze topology control in the context of the physical Signal-to-Interference-plus-Noise-Ratio (SINR) model, focusing on the question of how and how fast the links of a resulting topology can actually be realized over time. For this purpose, we dene and study a generalized ver- sion of the SINR model and obtain theoretical upper bounds on the scheduling complexity of arbitrary topologies in wire- less networks. Specically , we prove that even in worst-case networks, if the signals are transmitted with correctly as- signed transmission power levels, the number of time slots required to successfully schedule all links of an arbitrary topology is proportional to the squared logarithm of the number of network nodes times a previously dened static interference measure. Interestingly, although originally con- sidered without explicit accounting for signal collision in the SINR model, this static interference measure plays an im- portant role in the analysis of link scheduling with physi- cal link interference. Our result thus bridges the gap be- tween static graph-based interference models and the phys- ical SINR model. Based on these results, we also show that when it comes to scheduling, requiring the communication links to be symmetric may imply signican tly higher costs as opposed to topologies allowing unidirectional links.Proceedings of the 7th ACM Interational Symposium on Mobile Ad Hoc Networking and Computing, MobiHoc 2006, Florence, Italy, May 22-25, 2006; 01/2006 -
##### Conference Paper: Wireless Communication Is in APX.

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**ABSTRACT:**In this paper we address a common question in wireless communication: How long does it take to satisfy an arbitrary set of wireless communication requests? This problem is known as the wireless scheduling problem. Our main result proves that wireless scheduling is in APX. In addition we present a robustness result, showing that constant parameter and model changes will modify the result only by a constant.Automata, Languages and Programming, 36th International Colloquium, ICALP 2009, Rhodes, Greece, July 5-12, 2009, Proceedings, Part I; 01/2009

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