In this paper, we consider the channel assignment problem in single radio multi-channel mobile ad-hoc networks. Specifically, we investigate the granularity of channel assignment decisions that gives the best trade-off in terms of performance and complexity. We present a new granularity for channel assignment that we refer to as component level channel assignment. The strategy is relatively simple, and is characterized by several impressive practical advantages. We also show that the theoretical performance of the component based channel assignment strategy does not lag significantly behind the optimal possible performance, and perhaps more importantly we show that when coupled with its several practical advantages, it significantly outperforms other strategies under most network conditions.

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WLANs have become an important last-mile technology for providing internet access within homes and enterprises. In such indoor deployments, the wireless channel suffers from significant multipath scattering and fading that degrades performance. Beamforming is a smart antenna technology that adjusts the transmissions at the transmitter to reenforce the signals received through multiple paths at the receiver. However, doing this requires the accurate estimation of the channel coefficients at the receiver and its knowledge at the transmitter which off-the-shelf WiFi clients are incapable of doing. In this work, we develop a novel procedure that uses Received Signal Strength Indicator (RSSI) measurements at the receiver along with an intelligent estimation methodology at the transmitter to achieve beamforming benefits. Using experiments in an indoor office scenario with commercial WiFi clients, we show that the scheme achieves significant performance improvements across diverse scenarios.

It was conjectured in 1981 by the third author that if a graph G does not contain more than t pairwise edge-disjoint triangles, then there exists a set of at most 2t edges that shares an edge with each triangle of G. In this paper, we prove this conjecture for odd-wheel-free graphs and for 'triangle-3-colorable' graphs, where the latter property means that the edges of the graph can be colored with three colors in such a way that each triangle receives three distinct colors on its edges. Among the consequences we obtain that the conjecture holds for every graph with chromatic number at most four. Also, two subclasses of K 4 -free graphs are identified, in which the maximum number of pairwise edge-disjoint triangles is equal to the minimum number of edges covering all triangles. In addition, we prove that the recognition problem of triangle-3-colorable graphs is intractable.