A. Sen and M. L. Huson, A new model for scheduling packet radio networks, in Proc. 15th Ann. Joint Conference of the IEEE Computer and Communication Societies, 1996, pp. 1116--1124.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....same receiver which results in a scrambled signal. A number of authors have shown that the problem of minimizing the number of rounds required to realize communication between an arbitrary set of neighboring nodes is NP hard and or have provided heuristics for it [2, 3, 6, 12, 13] Sen and Huson [15] point out these previous authors assumed that the underlying graphs were arbitrary (and therefore the NP hardness easily follows from known graph coloring problems) They show that the problem remains NP hard when restricted to the domain of possible packet radio graphs and they give an O(n log ....

A. Sen and M. Huson, "A New Model for Scheduling Packet Radio Networks," Proc. 15th Annual Joint Conference of the IEEE Computer and Communication Societies INFOCOM, 1996, pp. 1116--1124.

....full knowledge of the network. In [1] the authors proved the existence of a family of n node networks of radius 2, for which any broadcast requires time Omega Gammame n) while in [4] it was proved that broadcasting can be done in time O(D log n) for any n node network of diameter D. In [11] the authors restricted attention to communication graphs that can arise from actual geometric locations of nodes in the plane. They proved that scheduling optimal broadcasting is NP hard even when restricted to such graphs and gave an O(n log n) algorithm to schedule an optimal broadcast when ....

A. Sen and M. L. Huson, A New Model for Scheduling Packet Radio Networks, Proc. 15th Annual Joint Conference of the IEEE Computer and Communication Societies (IEEE INFOCOM '96) (1996), 1116 - 1124. 22

....the communication graph of M d induced at time t, denoted GM (t) is defined as GM (t) N,E(t) where the edge (u,v)#E(t) if and only if v is at distance at most r from u at time t. If (u,v)#E(t) node v is said to be a neighbor of u at time t. GM (t) corresponds to a point graph as defined in [12]. In the next section, we consider probabilistic solutions to the following problem for stationary ad hoc networks: MINIMUM TRANSMITTING RANGE (MTR) what is the minimum value of r such that the resulting communication graph is connected Given the number of nodes, minimizing r while ....

A. Sen, and M. L. Huson, "A New Model for Scheduling Packet Radio Networks", Proc. IEEE Infocom '96, pp. 1116 -- 1124, 1996.

....v is in the transmitting range of u at time t, i.e. if and only if # d (D(u,t) D(v,t) #RA(u) where # d denotes the Euclidean distance in the d dimensional space. In this case node v is said to be a neighbor of u. Note that GM (RA,t) as defined here corresponds to the point graph as defined in [17]. The communication graph represents the set of all possible communication links in the network and is used to describe the desired properties of the wireless network. One common requirement is that the communication graph be strongly connected. Given a d dimensional network M d , a range ....

A. Sen, and M. L. Huson, "A New Model for Scheduling Packet Radio Networks", Proc. IEEE Infocom '96, pp. 1116 -- 1124, 1996.

....time a schedule giving broadcasting time O(D log 2 ) Gaber and Mansour [41] showed that for any packet radio network there is a schedule of broadcasting giving time O(D log 5 n) and that it can be found by a deterministic polynomial algorithm. Chlamtac and Kutten [18] and Sen and Hun [98] showed the NP completeness of nding optimal broadcasting schedules in packet radio networks, in particular it was shown in [98] that the problem remains NP complete even if the nodes are points in the plane and the reachability is determined by distances. Kirousis, Kranakis, Krizanc and Pelc ....

....is a schedule of broadcasting giving time O(D log 5 n) and that it can be found by a deterministic polynomial algorithm. Chlamtac and Kutten [18] and Sen and Hun [98] showed the NP completeness of nding optimal broadcasting schedules in packet radio networks, in particular it was shown in [98] that the problem remains NP complete even if the nodes are points in the plane and the reachability is determined by distances. Kirousis, Kranakis, Krizanc and Pelc [64] studied the problem of assigning transmission ranges to nodes located on a line so as to minimize the total power consumption ....

A. Sen, and M.L. Huson, A new model for scheduling packet radio networks, in Proc. 15th Joint Conference of the IEEE Computer and Communication Societies (INFOCOM), 1996, pp. 1116-1124.

....known deterministic constructive broadcasting algorithm can be adopted to perform oblivious gossiping in time O(n 3=2 ) Related work. O ine versions of communication problems were investigated in [6, 16] In particular, the NP completeness of nding optimal broadcasting schedules was shown in [5, 24]. Results on multi communication problems in radio networks can be found in [3, 12] Early work on distributed broadcasting in ad hoc radio networks includes [2] where there is given a randomized algorithm for broadcasting in expected time O(D log n log 2 n) A lower bound d 9 2 n) was ....

A. Sen, and M.L. Huson, A new model for scheduling packet radio networks, in Proc. 15th Joint Conference of the IEEE Computer and Communication Societies (INFOCOM), 1996, pp. 1116-1124.

....have full knowledge of the network. In [1] the authors proved the existence of a family of n node networks of radius 2, for which any broadcast requires time me 2 n) while in [21] it was proved that broadcasting can be done in time O(D log 5 n) for any n node network of diameter D. In [32] the authors restricted attention to communication graphs that can arise from actual geometric locations of nodes in the plane. They proved that scheduling optimal broadcasting is NP hard even when restricted to such graphs, and gave an O(n log n) algorithm to schedule an optimal broadcast when ....

A. Sen and M. L. Huson, A new model for scheduling packet radio networks, Proc. 15th Annual Joint Conference of the IEEE Computer and Communication Societies (IEEE INFOCOM'96) (1996), 1116 - 1124.

....n) where D is the network diameter. Diks et al. [10] gave ecient broadcasting algorithms for special types of known networks. It is also known that computing an optimal broadcast schedule for a given network is NP hard, even for points in the plane, where the graph is induced by node ranges, see [8, 26]. For networks with unknown topology, Bar Yehuda et al. [3] gave a randomized algorithm that achieves broadcast in expected time O(D log n log 2 n) This is very close to the lower bound of D log(n=D) by Kushilevitz and Mansour [18] and it matches this lower bound for a wide range of ....

A. Sen and M. L. Huson, A new model for scheduling packet radio networks, in Proc. 15th Ann. Joint Conference of the IEEE Computer and Communication Societies, 1996, pp. 1116-1124. 12

.... square of a graph is called distance 2 coloring, and has many applications, for example in approximating the Hessian matrices of certain nonlinear functions using a minimum number of gradient evaluations (See [14] or in frequency assignment (broadcast scheduling) in packet radio networks (See [15]) This problem is well studied and is proved to be NP complete even for planar graphs of bounded degree. See [13] for a summary of results. Another related problem is the antimatching problem. An antimatching in a graph G is a set A of edges of G such that any two edges in A are of distance at ....

A. Sen, and M. Huson, A new model for scheduling packet radio networks, in: Proc. IEEE INFOCOM'96, Vol. 3, 1116-1124. 11

....by the number of time slots in a frame. A schedule is a assignment of transceivers to the slots. Traditionally, a schedule is said to be optimal if it uses the minimum length frames. The problems associated with the construction of an optimal schedule have been studied extensively by researchers [1, 2, 3, 4]. Most of these studies dealt with the construction of two di erent types of schedules, broadcast schedules and link schedules, under two di erent types of interference, primary interference and secondary interference [2] In a broadcast schedule each (a) r a b a r b (b) r b r a c a b ....

....is within the transmission range of both a and b. In this case if a and b start simultaneous transmissions then c will be expected to receive from both a and b at the same time. We refer to this as type 2 primary interference. For the purpose of constructing an optimal schedule all prior research [1, 2, 3, 4] modeled a packet radio network as a graph, where a node in the graph represents a transceiver and there is a directed edge from the node v i to the node v j if the transceiver j is within the transmission range of the transceiver i. It may be noted that the resulting graph is a directed graph in ....

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A. Sen and M. Huson, A new model for scheduling packet radio networks, ACM/Baltzer Wireless Networks, vol. 3 (1997) no. 1, pp. 71-82.

....by the number of time slots in a frame. A schedule is a assignment of transceivers to the slots. Traditionally, a schedule is said to be optimal if it uses the minimum length frames. The problems associated with the construction of an optimal schedule have been studied extensively by researchers [1, 2, 3, 4]. Most of these studies dealt with the construction of two di erent types of schedules, broadcast schedules and link schedules, under two di erent types of interference, primary interference and secondary interference [2] In a broadcast schedule each (a) r a b a r b (b) r b r a c a b ....

....is within the transmission range of both a and b. In this case if a and b start simultaneous transmissions then c will be expected to receive from both a and b at the same time. We refer to this as type 2 primary interference. For the purpose of constructing an optimal schedule all prior research [1, 2, 3, 4] modeled a packet radio network as a graph, where a node in the graph represents a transceiver and there is a directed edge from the node v i to the node v j if the transceiver j is within the transmission range of the transceiver i. It may be noted that the resulting graph is a directed graph in ....

[Article contains additional citation context not shown here]

A. Sen and M. Huson, A new model for scheduling packet radio networks in Proc. IEEE INFOCOM '96, pp. 1116-1124.

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A. Sen and M. L. Huson, A new model for scheduling packet radio networks, in Proc. 15th Ann. Joint Conference of the IEEE Computer and Communication Societies, 1996, pp. 1116--1124.

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A. Sen and M.L. Huson, A new model for scheduling packet radio networks, 15th Annual Joint Conference of the IEEE Computer and Communication Societies, 1996, pp 1116-1124.

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A. Sen and M. L. Huson, "A new model for scheduling packet radio networks," in Proceedings of the 15th Annual Joint Conference of the IEEE Computer and Communication Societies (IEEE INFOCOM'96), vol. 3, Mar. 1996, pp. 1116--1124.

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A. Sen and M.L. Huson, A new model for scheduling packet radio networks, in Proc. 15th Ann., Joint Conference of the IEEE Comp. and Comm. Soc., 1996, pp 1116-1124.

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A. Sen and M. L. Huson, A new model for scheduling packet radio networks, in Proc. 15th Ann. Joint Conference of the IEEE Computer and Communication Societies, 1996, pp. 1116-1124.

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A. Sen, and M.L. Huson, A new model for scheduling packet radio networks, in Proc. 15th Joint Conference of the IEEE Computer and Communication Societies (INFOCOM), 1996, pp. 1116-1124.

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A. Sen and M. L. Huson, A new model for scheduling packet radio networks, in Proc. 15th Ann. Joint Conference of the IEEE Computer and Communication Societies, 1996, pp. 1116-1124. 10

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A. Sen and M.L. Huson, A new model for scheduling packet radio networks, 15th Annual Joint Conference of the IEEE Computer and Communication Societies, 1996, pp 1116-1124.

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A. Sen and M. L. Huson. A new model for scheduling packet radio networks. Wireless Networks, 3:71--82, 1997.

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Arunabha Sen and Mark L. Huson. A new model for scheduling packet radio networks. Wireless Networks, 3(1):71--82, 1997.

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A. Sen and M.L. Huson, A new model for scheduling packet radio networks, in Proc. 15th Ann., Joint Conference of the IEEE Comp. and Comm. Soc., 1996, pp. 1116-1124.

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A. Sen and M. L. Huson. A New Model for Scheduling Packet Radio Networks. In INFOCOM, 1996. 6

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A. Sen and M. L. Huson, A New Model for Scheduling Packet Radio Networks, Wireless Networks, 3 (1997), pp. 71--82.

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A. Sen, M. L. Huson, "A New Model for Scheduling Packet Radio Networks," Wireless Networks, Vol. 3, No. 1, March 1997.

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