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...er of link l has used up all the radios, i.e. � �C k∈E(b(l)) d=1 1 {k∈Md (t)} = Mb(l), or � �C k∈E(e(l)) d=1 1 {k∈Md (t)} = Me(l). Maximal schedules can be easily computed via a distributed algorithm =-=[30]-=-. For single-channel networks, such Maximal Scheduling algorithms have been shown to achieve an efficiency ratio of 1/K. However, for multi-channel networks with channel diversity, such algorithms can...

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...e a single schedule: the computation time increases with the network size. For instance, the maximal matching scheduling policy (MM), whose efficiency ratio is at least 1/2 [5], requires computations =-=[16]-=-. Lin and Rasool have recently proposed a constant-time scheduling policy that completes its scheduling after a fixed number of rounds [6]. This policy is proven to achieve an efficiency ratio up to 1...

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... of vertex u in G. We will make use of the maximum weight in the entire graph G, respectively in the neighborhood of a vertex u. For this purpose we define 2 It is worth noting that Hanckowiak et al. =-=[HKP01]-=- manage to give a O(log 4 ) time deterministic algorithm for the same model. 3 Note, that [KS00] and [CHS02] focus on self-stabilization, whereas [II86] does not. w max (G) and w max (u) E : w max (G)...

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...that every participant knows his/her gender. This assumption has not been exploited much in prior work on distributed, deterministic constant-time algorithms. We are only aware of Hańćkowiak et al. =-=[12]-=-, which shows that there is a constanttime algorithm for maximal matching in bicoloured bounded-degree graphs. Similarly to our algorithm, their algorithm does not need unique node identifiers; port n...

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...m is one of the main open problems in the area ([6]). However, an efficient distributed algorithm for the related Maximal Matching (MM) Problem is known due to Hańćkowiak, Karoński, and Panconesi. In =-=[4]-=- the three authors proved the following theorem. Theorem 1 ([4]). There is a distributed procedure Match which in O(log 4 n) many communication rounds in the synchronous, distributed model of computat...

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...y issues have been thoroughly studied in the literature, via the analysis of various construction problems, including coloring and MIS [2], [5], [26], [29], [31], [34], [37], MST [28], [39], matching =-=[20]-=-, [32], [33], [43], dominating set [27], [30], spanners [9], [12], [40], etc. For some problems (e.g., coloring [5], [26], [37]), there are still large gaps between the best known results on specific ...

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..., Ch. 1-2] for an extensive discussion of distributed models. Prior Work: The vertex coloring, MM, and MIS problems have been the subject of intensive research since the mid-1980s [1], [2], [3], [9], =-=[10]-=-, [11], [19], [20], [22], [23], [27], [30]. In 1986 Israeli and Itai [11] devised a randomized algorithm that computes an MM in O(log n) time with high probability, 2 and the same year Luby [22] and A...

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...) Th. 3 Det. O(∆)-edge coloring n, ∆ O(∆ǫ + log ∗ n) [7] O(∆ǫ + log ∗ n) Th. 5 Det. O(∆1+ǫ )-edge coloring n, ∆ O(log ∆ + log ∗ n) [7] O(log ∆ + log ∗ n) Th. 5 Det. Maximal Matching n or ∆ O(log 4 n) =-=[19]-=- O(log 4 n) Th. 6 Rand. MIS uniform O(log n) [30, 1] Rand. (2, 2(c + 1))-ruling-set n O(2c log 1/c n) [36] O(2c log 1/c n) Th. 7 Table 1: Comparison of LOCAL algorithms with respect to global paramete...