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tized access to assigned slots and exhibits high channel utilization in sparse network topologies [33] However, the results do not factor in any physical constraints, such as propagation delay and hardware switch-over time, which can significantly increase overall protocol overhead Furthermore, the handshaking mechanism employed in the contention interval does not support multicast packet transmissions The ABROAD protocol [34] accommodates multicast packets by altering the contention mechanism of ADAPT The RTS/CTS signaling in the priority interval does not need to be modified since its primary purpose is to simply inform nodes of activity in an assigned slot However, the use of a RTS/CTS dialogue fails in the contention interval due to the potential collision among the CTS responses, ie, information implosion ABROAD uses a form of negative feedback response to avoid this problem.

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Thus, a node responds with a negative CTS (NCTS) when a collision is detected in the contention interval or remains silent otherwise There are a few cases in which this type of handshaking fails, yet simulation results and analysis demonstrate that the probability of failure is small, eg, less than 4% in networks with low bit error rates [34] The AGENT protocol [35] integrates the unicast capabilities of ADAPT with the multicast capabilities of ABROAD The result is a generalized MAC protocol that is able to provide a full range of effective single-hop transmission services AGENT uses the same frame and slot structure of ADAPT, as well as the handshaking dialogue of the priority interval The control signaling in the contention interval is based on a combination of ADAPT and ABROAD.

Thus, to gain access to the transmission interval of a slot s, a source node i first transmits a RTS control packet This occurs at the beginning of the priority interval in an assigned slot, or the beginning of the priority interval, otherwise The reception of a RTS in the priority interval elicits a CTS response On the other hand, the reception of a RTS in the contention interval generates a CTS response only when it is associated with a unicast packet Any collision detected in the contention interval will cause a NCTS to be transmitted Once this initial control signaling is finished, a node can determine its eligibility to transmit its packet p in the transmission interval If s is assigned to i, then source node i is.

This cluster has the lowest total net sales, with a mean nearly one standard deviation below the overall average. Compared to cluster 1 (career clothes shoppers), this cluster tends to shop for more casual wear, having more than double the proportion of casual pants purchases and the highest overall amount spent on sweaters. This cluster is not interested in suits, with only 0.1% ever had bought one.

16.8 SHANNON MCMILLAN BREIMAN THEOREM (GENERAL AEP)

their lengths. Each edge is tested in that order (from shortest to longest) for inclusion in MST. If adding the edge to the already constructed graph does not create a cycle, the edge is then added to the constructed graph (that is, eventually to MST); otherwise it is not added. This construction also can be used to show that the connected unit graph contains MST as its subgraph (since edges whose length does not exceed the transmission radius will already connect the graph while constructing MST). Figure 10.3 shows an MST for a unit graph, with MST edges drawn in bold lines. When several edges are of the same length, the MST may not be unique. In order to have a unique structure for MST, one can label edges so that all edges become distinct, and edges of the same length can be compared. This can be achieved by introducing the weight of an edge AB as a record w(AB) jABj, min(id(A), id(B)), max(id(A), id(B))), where jABj is the length of AB, and id(A) and id(B) are unique identi ers of its endpoints, and jABj, min(id(A), id(B)), and max(id(A), id(B)) serve as the primary, secondary, and ternary keys in comparisons. Two edges are compared rst by their primary keys. If the primary keys are the same, secondary keys are used. If the secondary keys are also the same, the ternary keys are used. The de ned edge weights can also be applied to other structures, which are described in the following subsections, thus eliminating ambiguity and leading to some desirable characteristics (e.g., degree limitation). 10.5.2 Local Minimum Spanning Tree