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Coordinating Concurrent Transmissions:
A Constant-Factor Approximation of Maximum-Weight Independent Set in Local Conflict Graphs

Petteri Kaski, Aleksi Penttinen and Jukka Suomela

We study the algorithmic problem of coordinating transmissions in a wireless network where radio interference constrains concurrent transmissions on wireless links. We focus on pairwise conflicts between the links; these can be described as a conflict graph. Associated with the conflict graph are two fundamental network coordination tasks: (a) finding a nonconflicting set of links with the maximum total weight, and (b) finding a link schedule with the minimum total length. Our work shows that two assumptions on the geometric structure of conflict graphs suffice to achieve polynomialtime constant-factor approximations: (i) bounded density of devices, and (ii) bounded range of interference.We also show that these assumptions are not sufficient to obtain a polynomial-time approximation scheme (PTAS) for either coordination task. There exists a PTAS if we make an additional assumption: (iii) bounded range of radio transmissions.

Keywords: Geometric graphs, maximum-weight independent set, radio interference, routing, scheduling.

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