Improved flooding of broadcast messages using extended multipoint relaying

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1 Improved flooding of broadast messages using extended multipoint relaying Pere Montolio Aranda a, Joaquin Garia-Alfaro a,b, David Megías a a Universitat Oberta de Catalunya, Estudis d Informàtia, Mulimèdia i Teleomuniaió. Rambla del Poblenou 156, 818, Barelona, Spain b Institut Téléom. Dépt. Logique des Usages, Sienes Soiales et de l Information. Téléom Bretagne, Césson-Sévigné, CS 1767, 35576, Frane s: pma@uo.edu,joaquin.garia-alfaro@am.org,dmegias@uo.edu Abstrat A ommon operation in wireless ad ho networks is the flooding of broadast messages to establish network topologies and routing tables. The flooding of broadast messages is, however, a resoure onsuming proess. It might require the retransmission of messages by most network nodes. It is, therefore, very important to optimize this operation. In this paper, we first analyze the multipoint relaying (MPR) flooding mehanism used by the Optimized Link State Routing (OLSR) protool to distribute topology ontrol (TC) messages among all the system nodes. We then propose a new flooding method, based on the fusion of two key onepts: distane-enabled multipoint relaying and onneted dominating set (CDS) flooding. We present experimental simulations that show that our approah improves the performane of previous existing proposals. Key words: Wireless, Ad Ho Networks, Network Flooding, OLSR, MPR, CDS. 1. Introdution Wireless ad ho networks are generally onstruted without a preestablished struture. The nodes are in harge of disovering the system topology that will eventually allow them to work together. Two usual mehanisms to share information between the network nodes are: (1) point-to-point, in whih a node sends its messages towards a unique destination; and () flooding of broadast messages, in whih a node broadasts a message to all its neighbors, and those neighbors (or part of them) forward, reursively, the original message to eah node of the network [1]. The flooding proess an be used at several logial levels [, 3]. For instane, it an be used at the appliation level (when a node needs to send information to eah node of the network with a query or a delaration of data interest); or at the network ontrol level (for the onsolidation of the network struture, existene of nodes, or the harateristis and availability of the network links). These network ontrol messages must be sent not only during the network onsolidation stage, but also during all the network life (in order to update the nodes with environmental and network hanges). The resoure onsumption of flooding a network is, in general, very high. It needs several data transmission ations to be exeuted by high number of nodes in the network. For this reason, the optimization of any flooding mehanism is mandatory. In this sense, the Optimized Link State Routing (OLSR) protool [4] suggests an optimization for the flooding of broadast network onsolidation messages on ad ho networks based on multipoint relaying (MPR) flooding. Afterwards, it is possible to optimize the flooding of the remaining broadast messages by reorganizing the initial MPR flooding mehanism into a Conneted Dominating Set (CDS) struture. In this paper, we analyze these methods and transformations formally and then, we present the design of an alternative variant based on the use of an extended multipoint relaying flooding that improves the performane of the resulting CDS struture highly. We present a series of simulations that show the validity of our approah, and that reveal that our method onsiderably improves the performane of previous existing proposals. Our proposal is, moreover, ompatible with the forthoming evolutions of the OLSR protool (referred as OLSRv in the literature), by addressing the skethed extended quality riteria, suh as the seurity aspets of the resulting new protool [9, 1]. Notation Some basi notations are neessary to desribe the proposals and operations we present in this work: dist(i, j) : distane, in hops, from node i to node j. N 1 (x) = {y dist(x, y) = 1}: neighbors of a node, i.e., adjaent nodes. N * 1 (x) = N 1(x) {x}: neighbors of a node x, inluding the node itself. N * 1(X) = x X N * 1(x), neighbors of a set, inluding the set itself. N d * (X), neighbors of a { set at a distane in hops lower or X, if d =, equal to d: N d *(X) = N d 1 * (N 1(X)), * if d >. N d (X) = N d *(X) \ N d 1 * (X), neighbors of a set at a distane, in hops, stritly equal to d. Preprint submitted to Elsevier Otober, 1

2 Paper organization Setion presents the MPR seletion problem and desribes some appropriate implementation methods. Setion 3 analyzes the flooding proess of the OLSR protool and points out some drawbaks and early improvements. Setion 4 proposes our alternative variant. Setion 5 presents experimental evaluations and shows the performane results obtained with our proposal. Setion 6 loses the paper.. Multipoint relay (MPR) seletion The multipoint relay (MPR) seletion problem appears as an early stage of the OLSR routing protool. The original problem formulation is as follows: given a network node x, find a minimal subset of nodes, MPR(x), inluded in their immediate neighborhood with the harateristi that any node at a two-hop distane from x is a neighbor of, at least, a node in the MPR: MPR(x) N 1 (x), N (x) N 1 (MPR(x)). It is a quality objetive that MPR(x) must have minimal number of elements. It an be demonstrated, moreover, that finding the minimal solution is an NP-omplex problem [5], sine finding a solution is exponential in exeution time relative to the number of nodes in N 1 (x). The original MPR seletion problem an be generalized with the following formulation: given a set C of andidate nodes and a set T of target nodes, where all target nodes are neighbors of at least one andidate node (T N 1 (C)), find a subset MPR(C, T) inluded in C with minimal size and the harateristi that any node of T is a neighbor of (i.e., it is overed by) a node in MPR(C, T). It might not always be possible to fulfill these onditions if one node in T has not enough (i.e., m vg ) valid andidates in C. If that happens, the seond ondition must be relaxed to inlude all available neighbors. The resulting ondition is, hene, rewritten as follows: MPR(C, T, m vg ) C, y, y T N 1 (y) MPR(C, T, m vg ) m vg N 1 (y) C MPR(C, T, m vg )... MPR seletion as the solution of a restritions problem The MPR problem without extra overage an be seen as the solution of a boolean satisfiability problem. The variables of this problem are as many booleans as elements in C. The false value means that this element of C is not inluded in the set MPR(C, T), whereas the true value means that this element of C is inluded in MPR(C, T). These variables are denoted as, 1,, and so on. Eah node in T adds a new restrition to the set of possible solutions of the problem. This rule is an or ondition for the variables related to their neighbors in C. The objetive is to set to true a minimal number of variables x, suh that all rules are true. Assume the network depited in Figure 1, where gray nodes represent the set C and white nodes the set T. Preondition: T N 1 (C), MPR(C, T) C, T N 1 (MPR(C, T)). The quality riteria is to minimize the number of elements in MPR(C, T). From the formulation, it is straightforward to note that the original problem desribed in the OLSR standard is a partiular instane of this one, when C = N 1 (x) and T = N (x). The same onditions an be rewritten as follows: Preondition: T N 1 (C), MPR(C, T) C, y, y T N 1 (y) MPR(C, T) MPR seletion with extra overage In some network deployments, it is mandatory that any node in T must be neighbor of more than one node in the MPR set. This minimum number of nodes is refereed as the MPR overage (denoted here as m vg ) in the OLSR protool (f. RFC 366 [4], Setion 16). The previous problem formulation was the one for whih the m vg fator is equal to one. The generalized onditions for any given m vg are the following: MPR(C, T, m vg ) C, y, y T N 1 (y) MPR(C, T, m vg ) m vg. Figure 1: MPR problem example. We an observe that node 5 has two neighbors in C, nodes and. Thus, it generates the restrition. The remaining nodes in T generate the following restritions: t 5 :, t 6 :, t 7 :, t 8 :, t 9 : 1, t 1 : 1, t 11 : 1, t 1 : 1, t 13 : 3,...

3 This problem has one optimal solution 1. The ombination 3 4 is also a solution although it is not minimal..3. Solution of a restritions problem with extra overage When the MPR overage parameter (m vg for short) is greater than one (f. RFC 366 [4], Setion 16), the problem must be reformulated. Eah node in C is now assoiated to an integer variable in, 1. Eah node in T adds one restrition to the set of possible solutions of the form addition of their neighbors greater or equal than the restrition. The previous example, now with m vg =, i.e., t 5 : + = = 1, t 6 : + = = 1,... t 9 : = = 1,... has only one possible solution 1 = = 3 = 4 = 5 = 1. Let us observe, from this example, that: Several nodes in C are mandatory in the MPR set. If one target node has a number of neigbors in C equal or smaller than the requested overage, these neigbors are mandatory in the MPR. Looking at the example depited in Figure 1, and if m vg =, it is obvious that node 5 fores and to be inluded in the MPR subset. This situation is very likely to happen. Indeed, in most of the experimental simulations that we present in Setion 5, this kind of poorly overed nodes are, in most ases, almost the 9% of the total nodes in C. Several nodes in T generate the same restrition, suh as nodes 5, 6, 7 and 8 depited in Figure 1. When a speifi stratgey, like the greedy strategy used in the OLSR protool [5], needs to assign a weight to eah andidate, those restritions generated by more than one node have, in general, a weight equal to one (or equal to the number of nodes that generate this ondition). In the next setion we see how these alternatives impat in the size of the obtained MPR set..4. Pratial implementations In general, there will always exist several solutions to the MPR seletion problem. The minimal MPR set (i.e., the set with minimal ardinality) that solves the seletion problem (hereinafter denoted as min ) an be omputed by using a brute fore strategy. However, the omplexity of this approah is so high that, in pratie, it only applies for small networks. The approah relies on simply testing all possible subsets until finding the minimal one that fulfills all the requested onditions. Optimized versions of a brute fore seletion, based on searh and retry heuristis, exist [5]. These variants add to the proedure a sorted test of the subsets and rules to prune the searh tree. These solutions still present, however, a very ostly omplexity that renders the proess still impratial for average systems. 3 A more pratial solution, based on a greedy seletion strategy, is summarized in Funtion 1. Funtion 1 gives a solution of a size smaller than min (1+log( min )) [5], where min refers to the size of the minimal set solution. A worst ase example is given in Figure 1. The steps of Funtion 1, when it is applied to the network depited in Figure 1, are the following: i) In the first iteration, node is seleted, sine it has eight neighbors in T not yet overed (an amount of neighbors greater than node (=7), node 1 (=7), node 3 (=4), and node 4 (=)). Restritions related to nodes 5 to 1 are fulfilled and removed. ii) In the seond iteration, node 3 is seleted (four neighbors). iii) In the last iteration, node 4 is seleted. Funtion 1 omputes the set MPR(C, T) = {, 3,4}. Note that the solution is not minimal. An alternative solution with exatly two nodes (MPR(C, T) = {, 1}) is also valid. This drawbak an be handled if the nodes in T that have the same neighbors than a previous one are filtered. In the network given in Figure 1, all white nodes an be filtered by this rule exept nodes 5, 9, 13, 15, 17, and 18. If so, Funtion 1 provides the solution MPR(C, T) = {, 1} that is, moreover, minimal. It is, therefore, better to apply a greedy strategy ounting only the number of different rules that a node fulfills, instead of the total number of rules. In general, if two or more nodes in T generate the same restrition, only one instane of the restrition must be addressed. An alternative solution is too give priority to those nodes that are poorly overed by the system. For example, in the example depited by Figure 1, we an observe that some nodes (e.g., node 1) are mandatory, sine they have neighbors in T that no other neighbor overs. Thus, a logial first step is the addition to the MPR of this kind of nodes. Then, the following step is to analyze the ases where a node in T has only two possible andidates. It is mandatory that one of these two andidates gets inluded in the MPR. Therefore, it seems a onvenient approah to start solving this restrition before proeeding with easier ones (i.e., rules with more possible andidates). If so, a new proedure an be proposed. Funtion summarizes the new approah. The new seletion mehanism tries to fulfill all restritions starting by the most restritive one (i.e., smaller number of variables in the rule, i.e., smaller number of nodes in C neighbors of the nodes in T ) until the less restritive rule (e.g., the rule ontaining the largest amount of variables or andidates). If suh a rule has only one assoiated andidate, the orresponding node is added to the MPR. Otherwise, if the Funtion 1. Greedy MPR Seletion 1. Start with an empty MPR set.. Look for the andidate whih is present in more restritions not yet fulfilled by any other andidate. At least one restrition must be found. 3. The node is added to the MPR set, remove this node from the andidates list and remove all restritions already fulfilled. 4. Repeat Steps 1 and until all restritions are overed or no more andidates are available. 5. Return the resulting MPR set.

4 rule has more than one andidate, a heuristi method to selet the best andidate applies (e.g., a greedy-like seletion strategy). We an finally lose the setion by defining the standard MPR seletion proedure used in the OLSR protool as a mixture of greedy seletion and most restritive rule first seletion. An overview of the omplete proess is summarized in Funtion 3. Funtion. Most Restritive First MPR Seletion 1. Start with an empty MPR set.. Selet the target node in T whih has smaller number of neighbors in the andidate set C. Let C be the set of these neighbors. 3. Look for the node inluded in C that has maximum number of neighbors in the target set T. 4. Add the node found in previous step to the MPR set. Remove it from C. Derease the number of pending MPRs for all their neigbors in T. If the node has reahed the requested overage, remove it from T. 5. Repeat from the first step until T or C are empty. 6. Return the resulting MPR set. Funtion 3. Standard OLSR MPR Seletion 1. Start with an empty MPR set.. Apply Funtion, i.e., most restritive rules first, to selet those andidates whih appear in a rule of a size that is lower than the m vg parameter. Add the nodes to the MPR set. 3. Apply Funtion 1, i.e., greedy seletion, until all the remainder rules are fulfilled. 4. Return the resulting MPR set. Proedure 1. Soure-independent Flooding 1. The node whih originates the message sends it to all its neighbors.. A node whih reeives the message forwards it to all its neighbors if and only if it is the first time it reeives the message AND the node belongs to the predefined subset of forwarders. Otherwise, the message is not forwarded. 3. Step is repeated until no more forwards are exeuted for the message. Proedure. OLSR s Standard MPR Flooding 1. The node that originates the message sends it to all its neighbors.. A node that reeives the message forwards it to all its neighbors if and only if it is the first time it reeives the message AND the sender of the reeived message is inluded in the node list of MPR seletors. If not, the message is not forwarded. 3. Step is repeated until no more message forwards are exeuted. onsiderably redued. Proedure summarizes the soure-dependent flooding proess defined in the standard OLSR protool [4]. Notie that the flooding method proposed in Proedure has an important drawbak when applied to faulty networks. Indeed, if delays in the transmission of a message an lead, for instane, to a situation suh that not all the network nodes reeive the message, the propagation time an produe a failure in the flooding proess (even when the retransmission handles the failure of any single message). For instane, let us onsider the sample network depited by Figure. If we now as- 3. Flooding of broadast messages A ommon strategy for flooding messages on a network is the use of a soure-independent proedure (f. Proedure 1). A subset of nodes is in harge of retransmitting messages. The subset must satisfy that any of its nodes suessfully reahes any other node in the network by a path that stays entirely within the subset itself. The ost in resoures to flood the network is proportional to the size of the subset. Therefore, the goal is to obtain an optimal subset (in terms of size). OLSR addresses the problem in a different way. It uses the seletion of MPRs that we introdued in Setion, followed by a souredependent flooding strategy that works as follows: a node forwards a broadast message if and only if (1) it is the first time this message has been reeived by the node and () the adjaent sender of the message has seleted the node as one of its MPRs. In other words, any message is disarded if it has been previously reeived or if it is reeived by non MPR nodes [11]. The method is alled soure-dependent, sine a node deides to forward messages by taking into aount the origin of suh messages. Hene, the total amount of forwards in the network is Figure : Example of failure in a soure dependent flooding. 7

5 sume that MPR(3) = {1, 5} and MPR(4) = {, 6}, we observe that any error or delay in the reeption of a given message may ause that some network nodes do not reeive the message they intend to flood (even when suh a message has been suessfully retransmitted). The aforementioned problem of delays does not affet a soureindependent flooding. Therefore, it is possible to improve the flooding mehanism of OLSR by ombining soure-independent flooding and multipoint relaying. The approah presented by Adjih et al. in [1] is a proper example of this ombination. The solution proposes the transformation of the original MPR struture into a Conneted Dominating Set (CDS). A CDS derived from a set V of nodes is defined in the following equation N * 1(CDS) = V onneted(cds), where a reursive definition of onneted is: onneted ({x}), onneted (X {y}) onneted(x) y N 1 (X). By satisfying the properties of a valid CDS, the transformation allows the use of a soure-independent flooding strategy while keeping the total amount of forwards in the network onsiderably low. The transformation method in [1] requires a numeri labeling of the nodes. This an be based, for instane, on the IP address of the nodes. Let N min be the smallest node identifier of a neighborhood. Then, the Adjih et al. s method selets as forwarders of the underlying CDS those nodes that satisfy the following ondition: The node identifier orresponds to N min The node is in the MPR of an adjaent node with N min. A variation of the previous method was proposed by Wu et al. in [14, 15]. The first part of the previous or ondition is slightly modified to redue the CDS size: (The node identifier orresponds to N min The node has, at least, two unonneted neighbors) The node is in the MPR of an adjaent node with N min. morphology methods applied to graph optimization [13]. In this sense, our method generalizes the notion of multipoint relaying, by adding distane knowledge. This way, it improves the seletion of an optimized subset of forwarders, organized as an underlying CDS flooding struture. It implements, moreover, soure independent flooding of broadast messages, handling the problem of delayed forwards pointed out in Setion 3 (and whih is an inherent limitation of the soure dependent flooding method proposed in the OLSR protool). Proedure 3. Distane-enabled CDS Flooding 1. Selet one node of the network s.. Obtain the maximum dist(s, j) for all nodes, d max. Notie that the ase d max = (i.e., a single node network) an be ignored. Let a variable d with initial value d max Define a node set P of pending nodes and initialize it with all network nodes. 4. Find the solution of MPR d (s) = MPR(N d (s), N d+1 (s)) using any of the methods desribed in Part I of this doument. 5. All network nodes j at a distane d from s and whih are dominated by previous set MPR d (s) but do not belong to it are removed from P : j N 1 (MPR d (s)) j / MPR d (s) dist(s, j) = d. 6. If d > then repeat steps 4 and 5 for d d The resulting CDS is the union of all previously omputed MPR subsets, that is : CDS = MPR (s)... MPR dmax 1(s) Sample onstrution Assume the sample network depited in Figure 3. In the sequel, we summarize the exeution steps of Proedure 3 in order to ompute the underlying CDS-flooding struture for suh a network. The onstrution of this CDS-based forwarding subset, as a replaement of the multipoint relying set of any standard OLSR system, is laimed by the authors as a promising trade-off between minimization of forwarders and reliability of the exhanged information. Moreover, an inreased flood redundany an be ahieved by these methods if an MPR overage fator greater than one is settled during the MPR seletion state. In Setion 5, we show that this inrease leads, however, to a onsiderable performane overhead. In the sequel, we provide a new CDS-based flooding method, also ompatible with the addition of a dynami MPR overage parameter, that improves the performane of the standard OLSR flooding proedure, as well as the performane of the CDS-based flooding methods proposed in [1, 14, 15] Flooding method proposal In Proedure 3, we propose a new flooding method that optimizes the flooding proesses surveyed in Setion 3 and that allows the addition of extra overage (as suggested by Cuppens et al. in [7] for robustness reasons). Our solution gets inspiration from the use of mathematial 5 Figure 3: Sample network with node identifiers. Figure 4 shows the distane (in hops) from a node seleted as origin (node in this example) to all other nodes. The omputation of these distanes requires the knowledge of all the links in the system

6 3 3 t t 1 1 Figure 4: Proedure 3, Step. Distanes to node. Figure 6: Seond sequene, d = 1. t t t Figure 5: First sequene, d =. Figure 7: Final (trivial) sequene, d =. (already provided by an original onstrution of the OLSR system using multipoint relaying flooding). The maximal distane omputed is d max = 3. At distane d = 3, there are two nodes that are seleted as the targets of an MPR problem. The nodes at distane d = are the andidate nodes for this problem. In Figure 5, target nodes are labeled t and andidate nodes. Any of the MPR seletion funtions defined in Setion an now be used to solve the problem with T = {4, 8}, C = {, 3, 6,7}. The result is an MPR set equal to {3}. This is the first subset of nodes to be inluded in the final CDS. The next sequene handles nodes at distane d = (f. Figure 6). At this distane, we have four nodes. Two of them are already neighbors of a node in the CDS (nodes labeled by the symbol in the figure). Thus, the target nodes of the next MPR problem are the nodes in T = {, 3}. The andidate nodes are now all the nodes at distane d = 1, i.e., nodes in C = {1, 5}. Again, any valid MPR seletion funtion is used to solve the problem that results in the set MPR = {1}. This subset is added to the final CDS. Then, the proedure ontinues by handling the nodes at distane d = 1 (f. Figure 7). At this distane, the solution of the problem is now trivial. Note that although there are two nodes, only one of them is already neighbor of a node in the CDS. Thus, the only target node of the next MPR problem is in T = {1}. The only andidate node at distane d = is in C = {}. The result is MPR = {}. Therefore, node is added to the CDS. Figure 8 shows the final result, i.e., CDS = {, 1, 3}. We reall that, like in [1, 14, 15], our method requires an initial stage in whih a standard OLSR multipoint relaying flooding initially Figure 8: Resulting CDS subtopology derived from Proedure 3. sends TC messages to provide the list of links to eah node in the system. The ompleteness of this knowledge may impat in the quality of the obtained CDS. Let us also observe that a redution in the number of nodes of the CDS has a lear impat in the effiieny of the flooding proess (speially when nodes in the network are sparse). Thus, in sparse distributions of nodes, and when extra overage is required, some nodes are likely going to be poorly overed. If that ours, it an easily be solved by inreasing the MPR overage parameter. 6

7 5. Experimental simulations This setion presents experimental measurements that are performed to analyze and onfirm the main harateristis of the proesses desribed in previous setions. The experiments are exeuted in a simulation environment. Different onstrutions, with different densities of nodes and range of ommuniation, are deployed in a simulated unit square area. The deployment of nodes follows a random pattern with a uniform distribution in the x and y axes. The different MPR seletion funtions and flooding proedures are then applied to these networks. The series of experimental simulations are implemented using the Objetive Caml [6] programming language Evaluation of the MPR seletion funtions The objetive of our two initial simulations is simply to measure the average number of nodes inluded on the MPR sets omputed by the funtions we defined in Setion. A sample testbed (with five andidates and ten target nodes) is depited in Figure 9. The node that alulates the MPR sets in all three examples is node. The gray nodes represent the nodes seleted by node as MPRs. Eah set of experimental simulations ontains thirty andidate nodes and one hundred target nodes. All target nodes are, at least, linked to one andidate node. Additional links between targets and andidates nodes are reated at random. A network definition parameter, l, is used to fix the average number of links. It takes values from.4 (meaning more links between andidates and targets) to.15 (meaning a small number of links). One hundred different networks have been tested and averaged for eah value. Table 1 summarizes the results of the experimental simulations. Notie that the three MPR seletion methods provide almost the same ardinality MPR seletion method Average size of MPRs Funtion 1 (Greedy) 1.95 Funtion (Most restritive) 1.73 Funtion 3 (OLSR) 1.83 a) Greedy Seletion (f. Funtion 1) Table 1: Average MPR size vs. seletion funtions. In a seond experimental simulation, we measure the MPR overage parameter (m vg for short), applied to the standard OLSR seletion of MPRs (f. Funtion 3), and its effets on the size of the resulting MPRs. We do not show the results for Funtions 1 and, given that the differenes are minimal. The experimental setting is the same as in the previous series of simulations. The MPR overage fators are set to 1,, 3, and 4. Ten different networks are tested for eah set of parameters. The results of these tests are plotted in Figure 1. From the results of this seond series of simulations, we onlude that: (1) an inrease of the MPR overage fator in one unit inreases by, almost, a 5% the size of the resulting MPRs; and () that not all the nodes handle the requested MPR overage, i.e., there are always a onsiderably high amount of nodes that are poorly overed. b) Most Restritive First Seletion (f. Funtion ) m vg =1 m vg = m vg =3 m vg = Size of the MPR sets ) Standard OLSR seletion (f. Funtion 3) l=.4 l=.35 l=.3 l=.5 l=. l=.15 Link density Figure 9: Example of MPR set onstrutions based on three different MPR seletion methods. Gray nodes represent the nodes seleted as MPR nodes. Figure 1: MPR sizes for the OLSR seletion (Funtion 3) with extra overage. 7

8 5.. Handling delays with the standard MPR flooding The objetive of the following simulation is to analyze the sensibility of the standard MPR soure dependent flooding method (f. Proedure ) of the OLSR protool, when messages require extra retransmission due to reeption errors. Indeed, the simulations measure the ability of the OLSR proedure in ahieving this task. Eah simulation reates several random networks and omputes the retransmission of TC messages on eah network. The retransmission of the messages from a node towards its neighbors is onditioned by a probability of failure (provided as input parameters for eah simulation). In real senarios, we an assume that this failure might be aused by situations suh as interferenes, data orruption, or paket ollision in wireless networks. In ase of failure, the original message is disarded and its retransmission is queued. Although the message is never lost, this retransmission produes a delay in the reeption from some network nodes. This is the way how the simulations analyze the sensibility of the flooding proedure to the message delays. MPR-based CDS flooding methods proposed in [1, 14, 15] (f. Setion 3), and our proposal (f. Proedure 3). The results of the simulations are shown in Figure 1. The average number of nodes retransmitting the message is nodes with the MPR flooding method, for MPR-CDS method proposed by Adjih et al. [1], for MPR-CDS method proposed by Wu et al. [14, 15], and.54 for our proposed flooding method. Notie that our proposal presents a saving of resoures of almost a 5%. It also reahes a stable number of forwarders when the density of the network is high enough to over most of the unit square area. See, for example, the differenes from r =., n = 5 to n = 1 and to n = 15, where the number of forwarders when using our proposal remains stable whereas, in the other methods, this number ontinues inreasing proportionally to n. Similarly, our approah also reahes a stable number of forwards for ombinations r =.15, n = 15 and r =.15, n = MPR flooding Adjih et al. flooding Wu et al. flooding Our proposal Suessful floods 1% 95% 9% 85% Number of forwards % 75% n= r=.3 n=4 r=.3 n=5 n=1 n=15 r=. r=. r=. Network topology n=15 r=.15 n=3 r=.15 % 1% % 3% 4% 5% 6% 7% 8% 9% Delay probability Figure 11: Standard OLSR flooding with delayed TC message retransmissions. Figure 11 depits the results of ten thousand simulations, with different network definition parameters and delay probabilities. The flooding proess is onsidered to fail when, at least, one network node does not reeive the message. As expeted, an inrease in the probability of message delay produes an inrease in the number of networks for whih the flooding mehanism fails. We, therefore, onlude that if the physial medium of the network an produe this kind of transmission artifats, the use of the soure dependent flooding strategy used by the OLSR protool must ontain message aknowledgments or other protetion tehniques in order to assure that all the information is properly flooded Forwarding evaluation for eah flooding method The following series of simulations ompare the number of forward nodes when using the different flooding proedures. In all the simulations, n nodes are randomly plaed in a unit square area. If a node beomes isolated from all the remaining nodes and disonneted from the soure of the flooding, it is ignored. All the nodes have the same ommuniation range (denoted here as r). Bidiretional links between eah pair of nodes loser than r are available. The soure of the flooding is always the node with identifier. The simulations evaluate the flooding method of the standard OLSR protool (f. Proedure ), the Figure 1: Forwarding evaluation for eah flooding method (with m vg = 1). The following series of simulations ontinue the evaluation of the flooding methods when the MPR overage parameter inreases up to a fator of four. We reall that none of the methods an guarantee that the required MPR overage fator settled with values greater than one Method MPR overage Cost ratio MPR flooding [4] 1 35% Adjih et al. [1] 1 41% Wu et al. [14, 15] 1 37% Our proposal 1 1% MPR flooding [4] 56% Adjih et al. [1] 58% Wu et al. [14, 15] 54% Our proposal 35% MPR flooding [4] 3 68% Adjih et al. [1] 3 69% Wu et al. [14, 15] 3 65% Our proposal 3 45% MPR flooding [4] 4 73% Adjih et al. [1] 4 75% Wu et al. [14, 15] 4 71% Our proposal 4 5% Table : Forwarding evaluation for eah flooding method. 8

9 will be handled by all the nodes. Table summarizes the omplete series results. The ost riteria that we take into aount is the amount of forwarded messages that are generated for every method, normalized by the network size (denoted in Table as Cost ratio). Observe that in all four ases, our proposed method turns on a number of retransmissions that is muh smaller than all the other flooding methods Distane-enable MPR flooding with partial knowledge Most of the surveyed flooding proedures use only loal information about the network, i.e., the nodes need to know only their neighbors at one or two-hop distane. Some other methods need a global network overview, like all link-state protools. The input of these proesses is the link information database. This database an be omplete or partial. Inomplete link database means a partial knowledge of N d (x) whih redues the quality of the method. The amount of information whih a node stores about network links depends on the network protool. The usual situations are as follows: All nodes know all links. In protools like OLSR, only the MPRs do forward the topology ontrol (TC) messages. This means that only links from/to a node and their seleted MPRs are known by any node. MPR nodes broadast link information about all their neighbors, not only about the ones whih seleted them as MPRs. This option does not inrease the number of ontrol messages, only their size. When using our proposed method, it is relevant to measure how the different amount of TC information available at eah node affets the performane of the flooding proedure. Figure 13 shows how the differenes in the amount of available information affet the number of forwarders. Several networks with different sizes (denoted as n) and ommuniation ranges (denoted as r) are evaluated. Number of forwards n= r=.3 n=4 r=.3 n=5 r=. n=1 r=. Network topology n=15 r=. Complete MPRs N 1 of MPRs n=15 r=.15 Figure 13: Number of forwards when link database is not omplete. n=3 r=.15 Note that knowledge of full network information or knowledge of only MPR neighbors (muh better in the amount of ontrol messages) has a very similar performane in the flooding. In addition, a minimal OLSR ompliant network where nodes know only the links from MPR seletors to MPRs have a penalty of about 5% more forwards and the number of forwarders is, almost, the average between the optimal ase and the standard OLSR method. 6. Conlusion We have analyzed the formal desription of the MPR subset problem defined in the OLSR protool. We have presented some relevant methods for solving this problem, as well as some existing methods based on the MPR onept to perform an optimized flooding of messages over OLSR-based systems. We have then proposed a new flooding mehanism for suh systems. Simulations show that our proposal improves the performane of previous existing solutions. Indeed, it provides remarkable results, sine it signifiantly dereases the use of network resoures when flooding broadast messages over the system. Full adaptation of our proposal in some similar protools, taking into aount their intrinsi differenes and limitations, is a next step in our researh to onfirm the benefits of the approah that we have reported. Aknowledgments This work is partially supported by the Spanish Ministry of Siene and Innovation and the FEDER funds under the grants CONSOLIDER- INGENIO 1 CSD7-4 ARES and TSI C3-3 E-AEGIS, and the Institut TELECOM (programme Futurs et ruptures). Referenes [1] C. Adjih, P. Jaquet, and L. Viennot. Computing Conneted Dominated Sets with Multipoint Relays. Ad Ho & Sensor Wireless Networks, Marh 5. [] I. F. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayiri. Wireless Sensor Networks: A Survey IEEE Computers Networks, 38(4):393 4,. [3] I. F. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayiri, A survey on sensor networks IEEE Communiations Magazine, 4(8):1 114,. [4] T. Clausen and P. Jaquet. Optimized Link State Routing Protool (OLSR) IETF RFC 366, Otober 3. [5] G. Călinesu, I. I. Măndoiu, P. J. Wan, A. Z. Zelikovsky. Seleting forwarding neighbors in wireless ad ho networksmisbehaviors detetion to ensure availability on OLSR. Mobile Networks and Appliations, 9():11 111, 4. [6] Institut National de Reherhe en Informatique et en Automatique (IN- RIA). The Caml Language. [7] F. Cuppens, N. Cuppens-Boulahia, T. Ramard and J. Thomas. Misbehaviors detetion to ensure availability on OLSR LNCS 4864, pages , 7. [8] J. Harri, C. Bonnet, and F. Filali. OLSR and MPR: Mutual Dependenes and Performanes. Researh report RR-5-138, Institut Euréom, Marh 5. [9] U. Herberg and T. Clausen. Seurity Issues in the Optimized Link State Routing Protool Version (OLSRv). International Journal of Network Seurity & Its Appliations (IJNSA), ():16 181, April 1. [1] U. Herberg. 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