The Steiner Tree Problem with Delays: A compact formulation and reduction procedures

Leggieri, Valeria; Haouari, Mohamed; Triki, Chefi

doi:10.1016/j.dam.2011.07.008

Cited by 18 publications

(14 citation statements)

References 39 publications

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“…The SMT variant with delay constraints is also attractive to represent solutions for the multicast routing problem with QoS constraints. According to Oliveira and Pardalos (), the most studied version of the minimum Steiner tree problem applied to multicast routing with QoS constraint is that considering delays (Kompella et al., , ; Jia, ; Sriram et al., ; Raghavan et al., ; Leggieri et al., ). Combinations with other QoS constraints in other applications lead to even harder to solve problems.…”

Section: Related Workmentioning

confidence: 99%

Multicast routing under quality of service constraints for vehicular ad hoc networks: mathematical formulation and a relax‐and‐fix heuristic

Ribeiro

Santos

Souza

2018

Int Trans Operational Res

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In this paper, we investigate a multicast routing problem with quality of service constraints on ad hoc vehicular networks. An integer programming formulation for the problem is proposed that forms the basis of a relax-and-fix heuristic designed with the goal of producing feasible solutions of good quality. In addition, preprocessing procedures relying on simple and constrained shortest paths are developed that reduce the model size to the point of making it viable to compute. Computational experiments on benchmark instances generated to mimic realistic settings are reported. The results highlight the effectiveness of the relax-and-fix heuristic and the importance of the preprocessing routines for the computability of the proposed mathematical model. the most important intelligent transport systems are ad hoc vehicular networks or VANETs (Bitam and Mellouk, 2013). A VANET is a type of MANET where nodes are vehicles. There are two types of communication in VANETs: between vehicles (V2V-vehicle to vehicle) and between vehicles and infrastructured nodes (V2I-vehicle to infrastructure), also called RSU (roadside unit). Karim (2008) showed that VANETs are more suitable for vehicular communication because they have lower costs of implementation and communication even in places where there is no infrastructure. In addition, VANETs also have lower latency in data delivery when compared to other technologies such as 3G/4G networks and infostations.One possible application of VANETs consists in assisting vehicles to communicate and coordinate with each other, with the aim of avoiding any type of critical situation such as road accidents, traffic jams, and poor roads, as well as other applications such as speed control, detailed information on accidents for rescue teams, free passage of vehicles, and invisible obstacles. Another category of applications is information and entertainment for passengers and drivers. These are called applications for the comfort of drivers and passengers, such as Internet access, chats and interactive games between cars next to each other, free places for parking, and detailed information on fuel price, among others.In view of their high node mobility, the protocols of routing in vehicular ad hoc networks must be properly adapted and offer optimized routing. According to Peterson and Davie (2012), in a communication network there are three fundamental methods for data transmission: unicast, broadcast, and multicast. The multicast routing strategy reduces the communication cost and strongly explores the bandwidth and network resources, since the data packets can be transmitted to all destinations (members of the multicast group) by a single transmission, while with the unicast routing the source node sequentially transmits the same packet several times to different destinations and with the broadcast routing the source node transmits to all nodes in the network, whether they are interested or not in the message.In a VANET, as well as in other types of networks, many applications have special req...

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Section: Related Workmentioning

confidence: 99%

Multicast routing under quality of service constraints for vehicular ad hoc networks: mathematical formulation and a relax‐and‐fix heuristic

Ribeiro

Santos

Souza

2018

Int Trans Operational Res

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“…To solve it, the authors propose a Branch and Bound algorithm by using the Lagrangian Relaxation and heuristics to get lower and upper bounds in the Branch and Bound tree. A compact Mixed-Integer Program formulation with efficient reduction techniques can be found in [8]. In [9] the diameter-constrained minimum spanning tree variant (DM-STP) is defined.…”

Section: Related Workmentioning

confidence: 99%

Exact Algorithm to Solve the Minimum Cost Multi-Constrained Multicast Routing Problem

Molnar¹

2016

JCC

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The optimal solution of the multi-constrained QoS multicast routing problem is a tree-like hierarchical structure in the topology graph. This multicast route contains a feasible path from the source node to each of the destinations with respect to a set of QoS constraints while minimizing a cost function. Often, it is a tree. In other cases, the hierarchies can return several times to nodes and links of the topology graph. Similarly to Steiner problem, finding such a structure is an NP-hard problem. The usual tree and topology enumeration algorithms applied for the Steiner problem cannot be used to solve the addressed problem. In this paper, we propose an exact algorithm based on the Branch and Bound principle and improved by the Lookahead technique. We show relevant properties of the optimum hierarchy permitting efficient pruning of the search space. To our knowledge, our paper is the first to propose an exact algorithm for this non-trivial multi-constrained optimal multicast route computation. Simulations illustrate the efficiency of the proposed pruning operations. The analysis of the execution time shows that in simple topologies and with tight QoS constraints the exact algorithm requires relatively little execution time. With loose constraints the computation time cannot be tolerated even for off-line route computation. In these cases, the solution is close to a Steiner tree and heuristics can be applied. These results can serve as basis for the design of efficient, polynomial-time routing algorithms.

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“…This problem can be modelled as a Steiner tree problem, which is well known as a nondeterministic polynomial time‐complete problem . There are several algorithms that may be employed by multicast routing protocols to construct and maintain low‐cost multicast trees .…”

Section: Introductionmentioning

confidence: 99%

Subgraph selection over coded packet networks with multiple QoS parameters based on DEA

Raayatpanah

2016

Trans. Emerging Tel. Tech.

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Network coding is a generalisation of conventional routing methods that allows a network node to code information flows before forwarding them. Although network coding could be able to improve the throughput, reliability and security of multicast communications, it does not directly consider the quality of service requirements of multicast routing. In this paper, we study the problem of constructing a subgraph to allocate to coded packets, where several quality of service parameters, for example, bandwidth, delay, profit, packet loss and error rates, are associated with each arc in coded packet networks. For this purpose, we first evaluate the relative efficiency of arcs in the network based on data envelopment analysis techniques to send coded packets. Then, a linear programming model is introduced to determine coding subgraphs with respect to the relative efficiency of the arcs. The proposed approach is illustrated and evaluated through numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.

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The Steiner Tree Problem with Delays: A compact formulation and reduction procedures

Cited by 18 publications

References 39 publications

Multicast routing under quality of service constraints for vehicular ad hoc networks: mathematical formulation and a relax‐and‐fix heuristic

Multicast routing under quality of service constraints for vehicular ad hoc networks: mathematical formulation and a relax‐and‐fix heuristic

Exact Algorithm to Solve the Minimum Cost Multi-Constrained Multicast Routing Problem

Subgraph selection over coded packet networks with multiple QoS parameters based on DEA

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