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WDM **networks**. A light-hierarchy is a set of consecutive and directed fiber links occupying **the** same wavelength, which is rooted from **the** source and terminated at **the** destinations. Different from a light-tree, **the** light-hierarchy structure accepts **the** cycles introduced by **the** Cross Pair Switching capability of MI nodes, which enables an MI node to serve several destination nodes on **the** same wavelength through its different input and output pairs. Light-hierarchy structure overcomes **the** inherent drawback of **the** traditional light-tree structure, so that **the** splitting constraint is relaxed to some extent. This is why it outperforms **the** light-tree **in** term of cost. We proved that **the** **optimal** multicast structure for minimizing **the** wavelength channel cost is not a set of light-trees, but light-hierarchies. ILP formulations are developed and implemented to compute **the** **optimal** light-hierarchies. Numerical results verified that **the** light-hierarchy structure is **the** cost **optimal** solution for all-optical multicast **routing** with sparse splitting constraint.

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The number of transmissions required to deliver the I frame to the clients is thereby reduced from the size of the union of lost I frame packets to maximum number of I frame losse[r]

We may now compactly express the linear optimal control problem with linear state and control variable inequality constraints which represents the data communication network d[r]

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Abstract: Most of **the** existing **routing** protocols for ad hoc **networks** are designed to scale **in** **networks**
of a few hundred nodes. They rely on state concerning all links of **the** network or links on **the** route between a source and a destination. This may result **in** poor scaling properties **in** larger mobile **networks** or when node mobility is high. Using location information to guide **the** **routing** process is one of **the** most often proposed means to achieve scalability **in** large mobile **networks**. However, location- based **routing** is difficult when there are holes **in** **the** network topology. We propose a novel position- based **routing** protocol called Proximity Aware **Routing** for Ad-hoc **networks** (PARA) to address these issues. PARA selects **the** next hop of a packet based on 2-hops neighborhood information. We introduce **the** concept of “proximity discovery”. **The** knowledge of a node’s 2-hops neighborhood enables **the** protocol to anticipate concave nodes and helps reduce **the** risks that **the** **routing** protocol will reach a concave node **in** **the** network. Our simulation results show that PARA’s performance is better **in** sparse **networks** with little congestion. Moreover, PARA significantly outperforms GPSR for delivery ratio, transmission delay and path length. Our results also indicate that PARA delivers more packets than AODV under **the** same conditions.

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Related work. **In** **the** context of SRLG, basic network connectivity problems have been proven much more difficult to address than their usual counterparts. For instance, **the** problem of finding a “SRLG-shortest” st-path that is a path from node s to node t having **the** minimum number of risks has been proven N P -hard and hard to approximate **in** gen- eral (see [2]). However, **the** problem has been proven to be polynomial **in** two generic practical cases corresponding to localized failures: when all risks verify **the** star property [3] and when risks are of span 1 ; i.e. when a link is affected by at most one risk and links sharing a given risk form a connected component [2].

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I. I NTRODUCTION
Geographic **routing** [1]–[3], relying on **the** knowledge of geographic location information of nodes to make local route decisions, is a promising **routing** solution to **the** demand of developing efficient and scalable protocols **in** multihop wireless ad hoc **networks**. **In** recent years, with **the** significant advances of physical layer transmission techniques, cooper- ative communication for wireless **networks** has become an active research area due to its ability to create spatial diversity via node cooperation. There have been various cooperative diversity schemes **in** **the** literature [4]–[6]. However, most of them focus on **the** design of physical-layer cooperative relaying schemes, **in** which different issues such as signaling strategies, power allocation, relay selection, and bandwidth efficiency are taken into consideration to assess their physical layer performances.

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Springer Science+Business Media New York 2015
Abstract There is no doubt that P2P traffic mainly video traffic (e.g. P2P streaming, P2P file sharing, P2P IPTV) increases and will represent a significant percent of **the** total IP video traffic (80 percent by 2018 of **the** global IP traffic according forecasts). Peer-to-peer (P2P) is based on some main concepts such as mutualization of resources (e.g. data, programs, service) at Internet scale. It is also considered as one of **the** most important models able to replace **the** client-server model (e.g. for media streaming). Nevertheless, one of **the** fundamental problems of P2P **networks** is to locate node emplacements or resources and service location. Localisation problem is critical as there is no central server and churn rate can be high **in** some environments (high dynamicity). Lookup optimization **in** terms of number of hops or delay is not well considered **in** existing models, and still represents a real challenge. **In** this context and according to their specific characteristics and properties, De **Bruijn** graph based solutions constitute good candidates for lookup optimization. **In** this paper, we propose a new optimized model for lookup acceleration on P2P **networks** based on De **Bruijn** graph. Performance evaluations and simulation results show that our proposed approach is performant, compared to **the** main existing model.

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Each node i in the network maintains a topology table T i called its main topology table. A topology table is a list of the operational status of each link in the netw[r]

Mechanisms for explicit path selection are not included **in** most multicast distribution concepts. With explicit path selection, **the** sender of a multicast packet can explicitly select **the** distribution path (usually a tree) of a single multicast packet. This allows a sender selecting individual multi- cast trees for each single packet **in** order to react on events such as link breaks, node failures, congested links, and group member leaves. We propose that a sender of a multicast packet can select a backup multicast tree instead of **the** default multicast tree by inserting a fixed size iden- tifier to **the** multicast packet. A multicast delivery tree is typically established by multicast rout- ing protocols **in** case of IP multicast and by peer-to-peer protocols **in** case of application level multicast. Such a multicast delivery tree is then used for **the** distribution of multicast data. **The** selected backup multicast tree can then be used to immediately react on link failures without any delay caused by reestablishing a new multicast delivery tree for **the** new topology. Load balanc- ing can be achieved by using different trees simultaneously and can be applied when a particular link of **the** default multicast tree becomes congested or for increasing throughput.

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Many routing protocols have been proposed to keep the connectivity between nodes, including the AODV protocol (Ad Hoc On-Demand Distance Vector), which is maintained a[r]

as relays.
As illustrated by Fig. 5, **the** ad hoc communicating mode can sometimes be faster (**the** path is shorter) and should be used to speed up **the** **routing** process. To determine which mode to use, **the** node u first asks **the** value of hc(v) to AP (u). If AP (u) does not have this information, it requests it from other access points **in** **the** wired network. When u retrieves hc(v), it launches a broadcast with a Time-To-Live (TTL) equal to hc(A) + hc(B) − 1 to find a route **in** pure ad hoc mode (by using DSR for example). If v is not found by using this broadcast, it means that **the** path between them **in** ad hoc mode is longer than **the** one **in** infrastructure mode (i.e. hc(u, v) > hc(u) + hc(v)). **In** this case, **the** infrastructure mode will simply be used. By using this protocol, any two nodes can communicate to each other by knowing their routes and distances to access points.

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As noted **in** **the** previous section, EAN are a special case of k-trees, with k = d + 1. There actually exist several results concerning labelings of k-trees that allow to route by shortest paths (see for instance [41, 42]). However, those labelings are too general for our purpose. **In** particular, they are constructed using **the** fact that, at each step, a vertex is added to a particular k-clique. However, as mentioned **in** **the** previous section, **the** notion of step for **the** usual k-trees is a totally different concept than **the** one we use for EAN, and as a consequence, their labeling is not of **optimal** length. **In** **the** following, we develop a new and original labeling, especially designed for EAN, which is of **optimal** length and allows to route by shortest paths.

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1.4.2 Unicast **routing** with multiple metrics
Path computing problem for multiple metrics has been widely investigated **in** **the** literature. However **the** problem is inherently hard and a polynomial time algorithm may not exist. Finding a path with more than one constraint has been proven to be NP-complete [77]. Hence, **the** algorithms are distinguished by their type of solution, which can be exact, approximate or heuristic. Many works suggest that heuristic solution is **the** best way to treat them. Jaffe presented two algorithms for **the** MCP problem with two constraints [31]. **The** first one is a pseudo-polynomial-time algorithm, **the** second is a polynomial-time algorithm. It uses an objective function which combines **the** constraints to create a unique constraint. Then **the** algorithm finds **the** shortest path. **The** closest work is done by Chen and Nahrstedt **in** [11], who propose a heuristic algorithm for MCP. **The** idea is to first reduce **the** NP-complete problem to a simpler one, which can be solved **in** polynomial time, and then solve **the** new problem by using one of **the** following two algorithms. **The** first one is an extended Dijkstra’s shortest path algorithm (EDSP). **The** second one is an extended Bellman-Ford algorithm (EBF). Another algorithm to solve bandwidth-delay-constrained path was proposed by Wang and Crowcroft [77], which is based on two steps. First, all links that do not respect **the** bandwidth requirement are eliminated so **the** output is a feasible graph **in** term of bandwidth. **The** second consist **in** finding **the** shortest path **in** term of delay using Dijkstra’s algorithm.

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Reservation based scheduling dedicates chan-
nels exclusively for data transmission. For exam- ple, **in** (Wu, Ke, & Huang, 2007) potential senders use an ALOHA based random MAC scheme to send reservation requests to **the** central node. As reservation requests may collide and be lost, **the** reservation process needs an explicit confirmation. **The** scheduler (using its knowledge of **the** tuning time and delays) organizes asynchronous data transmissions between senders and destinations. A multicast scheduling algorithm called LBQA (Look Back Queue Access) is proposed. This algo- rithm favors multicast messages which can be sent immediately to all destinations. When there are no more all-receiver messages to transmit and while there are available data channels, **the** algorithm schedules also partitioned multicast messages (for an available subset of **the** destinations). **The** authors state that this scheduling algorithm can also be applied **in** PONs. **The** proposed architecture and **the** scheduling have some drawbacks. **The** scheduled time slot must allow sufficient time to tune **the** concerned transmitter and **the** receivers before data communication can start. This delay limits network performance. A large number of nodes **in** **the** domain can lead to heavy collisions

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Flow Cut
Fig. 6. Number of rounds generated **in** **the** optimization of cut and flow formulations.
225 nodes: from tenth of seconds to a few minutes for topologies with more than 100 nodes. On one hand, it allows to solve large-scale instances to optimality. On **the** other hand, **the** computational time is roughly **the** same as **the** formulation with flows [11]: sub-linear **in** **the** network size and linear **in** **the** gateways density. Moreover, one can see **in** Figure 6 that **the** number of generated rounds is decreased **in** comparison to **the** existing formulation with flows. This is better since **the** auxiliary program to generate new rounds is an ILP, and is related to **the** maximum independent set problem which is known to be N P -hard **in** general graphs. Indeed, if we consider a binary interference model, then a round is an independent set of **the** conflict graph, i.e. **the** graph where each node is a possible transmission **in** **the** network, and there exists a link between two of them if **the** corresponding transmissions are interfering.

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Another possibility arises when **the** time scale over which **the** fading states vary is much longer than **the** time that it takes to transmits a unit of information between two nodes. Assuming that **the** receiver is able to measure **the** channel state and there is a feedback mechanism for **the** receiver to send this information back to **the** transmitter, **the** transmitter can leverage this information to adjusted **the** transmitted power based on **the** present channel state. This approach, however, requires **the** channel state information at **the** transmitter. If we assume that such channel knowledge is not available at **the** transmitter, there is no way that **the** transmitter can adjust its power to compensate for very bad channel states. **The** appropriate model for **the** wireless link **in** this scenario is **the** capacity-versus-outage model, see [15], [16], [14]. **In** this model, **the** instantaneous capacity of a wireless link is treated as a random variable. A link is said to be **in** outage when **the** instantaneous capacity supported by **the** link is less than **the** transmission rate. **The** reliability of a link, i.e. **the** probability of correct reception at **the** receiver, is modeled as a function of **the** transmission rate, **the** transmitted power, **the** distance between **the** communicating nodes, and **the** channel fading state. By adjusting **the** transmission rate or power, **the** transmitter can control **the** probability of successful reception at its intended receiver.

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Our motivation stems from **the** fact that it has been shown that **the** break-even line length where optical communication lines become more effective than their electrical counterparts is less than 1cm, **in** terms of speed and power consumption [16]. Therefore, **the** use of opti- cal interconnections on-board is nowadays justified, and some studies even suggest that on-chip optical intercon- nects will soon be cost-effective [33]. Moreover, **the** emergence of cutting-edge technologies as Vertical Cav- ity Surface-Emitting Lasers (VCSELs) [15, 31], high sensibility optical transimpedance receivers [5], beam splitters [17, 18], micro-lenses [26], and holograms [7], makes possible **the** fabrication of complex optical com- munication **networks**.

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