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5411 IDS Module Placement for Noncollaborative Intrusion Detection In [80, 83] the authors address the problem of placement of intrusion detection modules considering ad hoc networks with multiple mobile intruders They consider networks in which each node is acting individually Cooperation amongst nodes is limited to sharing the recommendations Traf c capturing and analysis is done individually by every node In this work, the authors assume the use of misuse detection techniques, although some of the ideas are also applicable when the network is using the anomaly detection techniques The objective in this work is to maximize the detection probability given a constraint on the resources consumed for executing the IDS functions The proposed approach assumes that the nodes can monitor traf c promiscuously A node, after capturing traf c promiscuously, analyzes the captured traf c for any malicious signatures It is obvious that this leads to a signi cant wastage of network resources if every node has to execute the capture and analysis processes A more ef cient solution is to let a smaller subset of nodes monitor the traf c while ensuring that all of the network traf c is analyzed The question then is how to select this smaller subset of nodes that have exposure to all of the network traf c A concept that can be used to select this smaller subset of nodes is that of dominating sets A dominating set of nodes is the set of nodes such that these nodes along with the neighbors that each node can hear make up all the nodes in the network Identifying all the nodes that constitute the dominating set might not be suf cient for answering the question of where to place IDS capabilities This is because some of the nodes on the dominating set may not be able to execute IDS due to resource constraints Hence, the challenge is in selecting the set of nodes that constitute the dominating set while satisfying the resource constraints In addition, constraints on the capability of nodes to execute IDS imply that some of the traf c might not be analyzed for intrusions This implies that perfect detection might not be possible because it may not be possible to identify a complete dominating set where all nodes in the dominating set are IDS capable Hence, the authors seek to maximize the detection rate To understand these concepts, consider Figure 52 Here we consider ve nodes A node is denoted by a vertex and an edge represents the neighbor relation Thus an edge between two nodes indicates that the nodes are neighbors We would like to remark here that a node is able to receive all packets transmitted by its neighbor although it may not receive all packets received by its neighbor Thus a dominating set in this context is the set of nodes such that these nodes can hear all the traf c transmitted by their neighbors One such example of a dominating set is the set of nodes [v1, v3, v5] since these nodes along with their neighbors constitute the entire network But note that this is not the minimum dominating set, that is, a dominating set with the least number of members [v2, v4] corresponds to a minimum dominating set In such a case, executing the IDS on the nodes that constitute the minimum dominating set is suf cient to capture all the network traf c and hence achieve perfect detection Now assume that the shaded nodes v2, v3, v4 are incapable of executing IDS In this case the set of nodes that can execute IDS is [v1, v5], but as is obvious, this set of nodes will not be able to detect any malicious traf c originating from v3 to either of its neighbors This implies that it is not possible to achieve perfect detection Note that a.

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when m is large, X and s will essentially have the same form Second, because of the rst property, it allows us to decide where the process will be irregular and where it will be smooth Figure 1114 displays an example of SRMP with controlled shapes

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Figure 1114 (a) SRMP with g(Z) = Z (black), and controlling shape function (gray); (b) the same SRMP (black) with estimated H lder exponent (gray)

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It is then possible to obtain a ne model for RR traces based on the following ingredients: an s function, that describes the overall shape of the trace, and in particular the nycthemeral cycle; a g function whose role is to ensure that the correct relation between the heart rate and its regularity is maintained at all times The shape s is estimated from the data in the following way; for each RRi time series, histograms of both the signal and its exponent are plotted, and modeled as a sum of two Gaussians, as represented in Figure 1115

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