Minimum-cost Multicast Research Articles

ILP formulation of the exact solution of multi-constrained minimum cost multicast

Multimedia applications such as videoconferencing and collaborative applications require the satisfaction of several Quality of Service constraints (QoS). The routing with respect to QoS constraints was proposed in order to satisfy the user requirement and guarantee a certain level of performance to a data flow. As the communication architecture of these applications is often multicasting, the problem of finding a multicast route satisfying the QoS constraints proves to be challenging. In this paper we propose an Integer Linear Program (ILP) for finding the multicast route respecting a set of QoS constraints with minimum cost. Since the problem is NP-hard, we propose an efficient pretreatment algorithm (ArcReduce) to accelerate the resolution time. The pretreatment process can even answer in polynomial time, whether the problem has a solution or not, before starting the resolution process. The computation of the exact solution also allows for comparison of the heuristic solutions to the exact solution. We conduct an analysis of the ILP and the ArcReduce with various sizes of input data regarding the execution time, the success rate and the quality of the generated multicast route.

A robust optimization approach for multicast network coding under uncertain link costs

Network coding is a technique that can be used to improve the performance of communication networks by performing mathematical operations at intermediate nodes. An important problem in coding theory is that of finding an optimal coding subgraph for delivering network data from a source node throughout intermediate nodes to a set of destination nodes with the minimum transmission cost. However, in many real applications, it can be difficult to determine exact values or specific probability distributions of link costs. Establishing minimum-cost multicast connections based on erroneous link costs might exhibit poor performance when implemented. This paper considers the problem of minimum-cost multicast using network coding under uncertain link costs. We propose a robust optimization approach to obtain solutions that protect the system against the worst-case value of the uncertainty in a prespecified set. The simulation results show that a robust solution provides significant improvement in worst-case performance while incurring a small loss in optimality for specific instances of the uncertainty.

Novel Approach to Sub-graph Selection over Coded Wireless Networks with QoS Constraints

ABSTRACTIn this paper, we study the problem of minimum-cost multicast with network coding, while the maximum end-to-end weight, such as delay, throughput, and security, along paths from the source to each destination is bounded by a constant. We propose a path-based mixed integer programming model for the problem and show that the problem is non-deterministic polynomial (NP)-hard. We apply a column-generation approach to solve this model, where the problem is decomposed into a master linear programming problem and several integer programming sub-problems. We also introduce an approach to get a lower bound of optimal solution. Simulation results demonstrate that using of column-generation approach in combination with network coding to solve this problem can enhance the efficiency of final solution, no matter of the size of underlying network.

Minimum Cost Multicast Routing Using Ant Colony Optimization Algorithm

Multicast routing (MR) is a technology for delivering network data from some source node(s) to a group of destination nodes. The objective of the minimum cost MR (MCMR) problem is to find an optimal multicast tree with the minimum cost for MR. This problem is NP complete. In order to tackle the problem, this paper proposes a novel algorithm termed the minimum cost multicast routing ant colony optimization (MCMRACO). Based on the ant colony optimization (ACO) framework, the artificial ants in the proposed algorithm use a probabilistic greedy realization of Prim’s algorithm to construct multicast trees. Moving in a cost complete graph (CCG) of the network topology, the ants build solutions according to the heuristic and pheromone information. The heuristic information represents problem-specific knowledge for the ants to construct solutions. The pheromone update mechanisms coordinate the ants’ activities by modulating the pheromones. The algorithm can quickly respond to the changes of multicast nodes in a dynamic MR environment. The performance of the proposed algorithm has been compared with published results available in the literature. Results show that the proposed algorithm performs well in both static and dynamic MCMR problems.

Fast and adaptive evolutionary algorithm for minimum-cost multicast with network coding

Presented is a fast and adaptive evolutionary algorithm that minimises the resource consumption of network coding while achieving the target multicast rate. To this end, infeasible individuals adaptively participate as well in searching for better solutions, and all individuals are evaluated in an opportunistic manner. The empirical results have adduced grounds for the effectiveness of the approach.

Distributed Algorithms for Minimum Cost Multicast With Network Coding

Network coding techniques are used to find the minimum-cost transmission scheme for multicast sessions with or without elastic rate demand. It is shown that in wireline networks, solving for the optimal coding subgraphs in network coding is equivalent to finding the optimal routing scheme in a multicommodity flow problem. A set of node-based distributed gradient projection algorithms are designed to jointly implement congestion control/routing at the source node and virtual routing at intermediate nodes. The analytical framework and distributed algorithms are further extended to interference-limited wireless networks where link capacities are functions of the signal-to-interference-plus-noise ratio (SINR). To achieve minimum-cost multicast in this setting, the transmission powers of links must be jointly optimized with coding subgraphs and multicast input rates. Node-based power allocation and power control algorithms are developed for the power optimization. The power algorithms, when iterated in conjunction with the congestion control and routing algorithms, converge to the jointly optimal multicast configuration. The scaling matrices required in the gradient projection algorithms are explicitly derived and are shown to guarantee fast convergence to the optimum from any initial condition.

Optimizing Patching‐based multicast for video‐on‐demand in wireless mesh networks

AbstractIn this work, we study the application of video‐on‐demand (VoD) in wireless mesh networks (WMN), a next generation edge technology to provide broadband data access in residential, business and even city‐wise networks. We adopt a Patching‐based multicast technique to better utilize the bandwidth resources in the mesh network. We optimize the Patching‐based multicast by addressing two critical problems, namely, the Minimum Cost Multicast Tree (MCMT) problem and the Maximum Benefit Multicast Group (MBMG) problem. The MCMT problem is to find a MCMT in the network. We show that finding such a tree in the WMN can be formulated as a graph theory problem, which is to find the tree with minimum number of non‐leaf nodes, and which spans all the nodes in the multicast group. We further prove the problem is NP‐hard and propose a fast greedy algorithm to accommodate the real‐time feature of the VoD application. We solve the MBMG problem by minimizing the communication of a Patching group in the entire network. A Markov model is proposed to capture the growth of the multicast group in the WMN. Simulation study results validate the proposed solutions of the two problems. Copyright © 2009 John Wiley & Sons, Ltd.

Enforcing Minimum-Cost Multicast Routing against Selfish Information Flows

We study multicast in a noncooperative environment where information flows selfishly route themselves through the cheapest paths available. The main challenge is to enforce such selfish multicast flows to stabilize at a socially optimal operating point incurring minimum total edge cost, through appropriate cost allocation and other economic measures, with replicable and encodable properties of information flows considered. We show that known cost allocation schemes are not sufficient. We provide a shadow-price-based cost allocation for networks without capacity limits and show that it enforces minimum-cost multicast. This improves previous result where a 2-approximate multicast flow is enforced. For capacitated networks, computing cost allocation by ignoring edge capacities will not yield correct results. We show that an edge tax scheme can be combined with a cost allocation to strictly enforce optimal multicast flows in this more realistic case. If taxes are not desirable, they can be returned to flows while maintaining weak enforcement of the optimal flow. We relate the taxes to VCG payment schemes and discuss an efficient primal-dual algorithm that simultaneously computes the taxes, the cost allocation, and the optimal multicast flow, with potential of fully distributed implementations.

Minimum-cost multicast over coded packet networks

We consider the problem of establishing minimum-cost multicast connections over coded packet networks, i.e., packet networks where the contents of outgoing packets are arbitrary, causal functions of the contents of received packets. We consider both wireline and wireless packet networks as well as both static multicast (where membership of the multicast group remains constant for the duration of the connection) and dynamic multicast (where membership of the multicast group changes in time, with nodes joining and leaving the group). For static multicast, we reduce the problem to a polynomial-time solvable optimization problem, and we present decentralized algorithms for solving it. These algorithms, when coupled with existing decentralized schemes for constructing network codes, yield a fully decentralized approach for achieving minimum-cost multicast. By contrast, establishing minimum-cost static multicast connections over routed packet networks is a very difficult problem even using centralized computation, except in the special cases of unicast and broadcast connections. For dynamic multicast, we reduce the problem to a dynamic programming problem and apply the theory of dynamic programming to suggest how it may be solved.

An iterative algorithm for delay-constrained minimum-cost multicasting

The bounded shortest multicast algorithm (BSMA) is presented for constructing minimum-cost multicast trees with delay constraints. The BSMA can handle asymmetric link characteristics and variable delay bounds on destinations, specified as real values, and minimizes the total cost of a multicast routing tree. Instead of the single-pass tree construction approach used in most previous heuristics, the new algorithm is based on a feasible-search optimization strategy that starts with the minimum-delay multicast tree and monotonically decreases the cost by iterative improvement of the delay-bounded multicast tree. The BSMA's expected time complexity is analyzed, and simulation results are provided showing that BSMA can achieve near-optimal cost reduction with fast execution.