Minimum-power multicast routing in static ad hoc wireless networks

Wieselthier et al. (2000) proposed three greedy heuristics for Min-Power Asymmetric Broadcast Routing: SPT (shortest-path tree), MST (minimum spanning tree), and BIP (broadcasting incremental power). Wan et al. (2001) proved that SPT has an approximation ratio of at least (n/2) where n is the total number of nodes, and both MST and BIP have constant approximation ratios. Based on the approach of pruning, Wieselthier et al. also proposed three greedy heuristics for Min-Power Asymmetric Multicast Routing: P-SPT (pruned shortest-path tree), P-MST (pruned minimum spanning tree), and P-BIP (pruned broadcasting incremental power). In this paper, we first prove that the approximation ratios of these three heuristics are at least (n-1/2),n-1, and n-2-o(1), respectively. We then present constant-approxiation algorithms for Min-Power Asymmetric Multicast Routing. We show that any /spl rho/-approximation Steiner tree algorithm gives rise to a c/spl rho/-approximation heuristic for Min-Power Asymmetric Multicast Routing, where c is a constant between 6 and 12. In particular, the Takahashi-Matsuyama Steiner tree heuristic leads to a heuristic called SPF (shortest-path first), which has an approximation ratio of at most 2c. We also present another heuristic, called MIPF (minimum incremental path first), for Min-Power Asymmetric Multicast Routing and show that its approximation ratio is between (13/3) and 2c. Both SPF and MIPF can be regarded as an adaptation of MST and BIP, respectively, in a different manner than pruning. Finally, we prove that any /spl rho/-approximation Steiner tree algorithm also gives rise to a 2/spl rho/-approximation algorithm for Min-Power Symmetric Multicast Routing.     

Evaluation of multicast routing algorithms for real-timecommunication on high-speed networks

Multicast (MC) routing algorithms capable of satisfying the quality of service (QoS) requirements of real-time applications will be essential for future high-speed networks. We compare the performance of all of the important MC routing algorithms when applied to networks with asymmetric link loads. Each algorithm is judged based on the quality of the MC trees it generates and its efficiency in managing the network resources. Simulation results over random networks show that unconstrained algorithms are not capable of fulfilling the QoS requirements of real-time applications in wide-area networks. Simulations also reveal that one of the unconstrained algorithms, reverse path multicasting (RPM), is quite inefficient when applied to asymmetric networks. We study how combining routing with resource reservation and admission control improves the RPM's efficiency in managing the network resources. The performance of one semiconstrained heuristic, MSC, three constrained Steiner tree (CST) heuristics, Kompella, Pasquale, and Polyzos (1992), constrained adaptive ordering (CAO), and bounded shortest multicast algorithm (BSMA), and one constrained shortest path tree (CSPT) heuristic, the constrained Dijkstra heuristic (CDKS) are also studied. Simulations show that the semiconstrained and constrained heuristics are capable of successfully constructing MC trees which satisfy the QoS requirements of real-time traffic. However, the cost performance of the heuristics varies. The BSMA's MC trees are lower in cost than all other constrained heuristics. Finally, we compare the execution times of all algorithms, unconstrained, semiconstrained, and constrained     

Improved neural heuristics for multicast routing

Future networks must be adequately equipped to handle multipoint communication in a fast and economical manner. Services requiring such support include desktop video conferencing, tele-classrooms, distributed database applications, etc. In networks employing the asynchronous transfer mode (ATM) technology, routing a multicast is achieved by constructing a minimum cost tree that spans the source and all the destinations. When the network is modeled as a weighted, undirected graph, the problem is that of finding a minimal Steiner tree for the graph, given a set of destinations. The problem is known to be NP-complete. Consequently, several heuristics exist which provide approximate solutions to the Steiner problem in networks, We show how the random neural network (RNN) can be used to significantly improve the quality of the Steiner trees delivered by the best available heuristics which are the minimum spanning tree heuristic and the average distance heuristic. We provide an empirical comparison and find that the heuristics which are modified using the neural network yield significantly improved trees     

Multicast tree generation in networks with asymmetric links

We formulate the problem of multicast tree generation as one of computing a directed Steiner tree of minimal cost. In this context, we present a polynomial-time algorithm that provides for trade-off selection, using a single parameter κ, between the tree-cost (Steiner cost) and the run time efficiency. Further, the same algorithm may be used for delay optimization or tree-cost minimization simply by configuring the value of κ appropriately. We present theoretical and experimental analysis characterizing the problem and the performance of our algorithm. Theoretically, we show that it is highly unlikely that there exists a polynomial-time algorithm with a performance guarantee of constant times optimum cost, introduce metrics for measuring the asymmetry of graphs, and show that the worst-case cost of the tree produced by our algorithm is, at most, twice the optimum cost times the asymmetry, for two of these asymmetry metrics. For graphs with bounded asymmetry, this gives constant times optimum performance guarantee. We also show that three well-known algorithms for (undirected) Steiner trees are but particular cases of our algorithm. Our experimental study shows that operating at a low κ gives nearly best possible expected tree cost while maintaining acceptable run-time efficiency     

Multicriteria Steiner tree with the cost of Steiner vertices

The multicriteria problem of constructing the Steiner tree with consideration for the cost of additional Steiner vertices is studied. Formulations of the problems of constructing the covering Steiner trees and algorithmic approaches are described. The engineering formulation of the problem is aimed at constructing a telecommunications network with allowance for the spatial distribution of radio interferences. An approach to solving the formulated milticriterion problem on the basis of combination of two solving schemes is proposed: (1) the basic scheme for constructing a covering Steiner tree on the basis of clustering the vertices of the initial graph and (2) the general scheme for constructing the covering Steiner trees with allowance for the number of additional vertices and calculation of the Pareto-efficient solutions. A module based on the modified Prim’s algorithm for constructing a multicriteria covering tree is additionally used. The vertices of the initial graph are clustered on the basis of a hierarchical algorithm. Examples of a computational experiment on constructing the multicriteria Steiner trees are given.     

Utilizing Redundancy for Timing Critical Interconnect

Conventionally, the topology of signal net routing is almost always restricted to Steiner trees, either unbuffered or buffered. However, introducing redundant paths into the topology (which leads to non-tree) may significantly improve timing performance as well as tolerance to open faults and variations. These advantages are particularly appealing for timing critical net routings in nanoscale VLSI designs where interconnect delay is a performance bottleneck and variation effects are increasingly remarkable. We propose Steiner network construction heuristics which can generate either tree or non-tree with different slack-wirelength tradeoff, and handle both long path and short path constraints. We also propose heuristics for simultaneous Steiner network construction and buffering, which may provide further improvement in slack and resistance to variations. Furthermore, incremental non-tree delay update techniques are developed to facilitate fast Steiner network evaluations. Extensive experiments in different scenarios show that our heuristics usually improve timing slack by hundreds of pico seconds compared to traditional approaches. When process variations are considered, our heuristics can significantly improve timing yield because of nominal slack improvement and delay variability reduction.     

一种改进的Steiner树启发式算法

最小Steiner树问题是NP完全问题，关于Steiner问题的启发式算法的研究具有重要理论和实际意义。本文在MPH算法基础上，对于经过某些关键节点的短路径优先考虑，提出了KBMPH算法，从而实现更多链路的共享。在随机网络上的仿真结果表明，极大多数情况下，在准Steiner树的网络费用KBMPH算法优于MPH算法，KBMPH算法的复杂度为O（n^3）。     

Distributed center-location algorithms

Recent multicast routing protocol proposals such as protocol independent multicast (PIM) and core-based trees (CBT) have been based on the notion of group-shared trees. Since construction of a minimal-cost tree spanning for all members of a group is difficult, they rely on center-based trees and distribute packets from all sources over a single shortest-path tree rooted at some center. PIM and CBT provisionally use administrative selection or simple heuristics for locating the center of a group but do not preclude the use of other methods that provide an ordered list of centers. Other previously proposed heuristics typically require knowledge of the complete network topology, a requirement which is not always practical for a distributed problem such as Internet routing. We investigate the problem of finding a good center in a distributed fashion, study various heuristics for automating center selection, and examine their applicability to real-world networks. We also propose several new algorithms which we feel to be more practical than existing methods. We present simulation results on hierarchical and nonhierarchical networks showing that of the methods potentially feasible in the Internet multicast backbone, ours offer the best results in terms of cost and delay, and they incur low overhead     

Distributed algorithms for multicast path setup in data networks

Establishing a multicast tree in a point-to-point network of switch nodes, such as a wide-area asynchronous transfer mode (ATM) network, can be modeled as the NP-complete Steiner problem in networks. In this paper, we introduce and evaluate two distributed algorithms for finding multicast trees in point-to-point data networks. These algorithms are based on the centralized Steiner heuristics, the shortest path heuristic (SPH) and the Kruskal-based shortest path heuristic (K-SPH), and have the advantage that only the multicast members and nodes in the neighborhood of the multicast tree need to participate in the execution of the algorithm. We compare our algorithms by simulation against a baseline algorithm, the pruned minimum spanning-tree heuristic that is the basis of many previously published algorithms for finding multicast trees. Our results show that the competitiveness (the ratio of the sum of the heuristic tree's edge weights to that of the best solution found) of both of our algorithms was, on the average, 25% better in comparison to that of the pruned spanning-tree approach. In addition, the competitiveness of our algorithms was, in almost all cases, within 10% of the best solution found by any of the Steiner heuristics considered, including both centralized and distributed algorithms. Limiting the execution of the algorithm to a subset of the nodes in the network results in an increase in convergence time over the pruned spanning-tree approach, but this overhead can be reduced by careful implementation     

Multicast routing, load balancing, and wavelength assignment ontree of rings

There are two steps to establish a multicast connection in WDM networks: routing and wavelength assignment. The shortest path tree (SPT) and minimum spanning tree (MST) are the two widely used multicast routing methods. The SPT method minimizes the delay from the source to every destination along a routing tree, and the MST method is often used to minimize the network cost of the tree. Load balancing is an important objective in multicast routing, which minimizes the maximal link load in the system. The objective of wavelength assignment is to minimize the number of wavelengths used in the system. This paper analyzes the performance of the shortest path tree (SPT) and minimum spanning tree (MST) methods in the tree of ring networks, regarding the performance criteria such as the delay and network cost of the generated routing trees, load balancing, and the number of wavelengths required in the system. We prove that SPT and MST methods can not only produce routing trees with low network costs and short delays, but also have good competitive ratios for the load balancing problem (LBP) and wavelength assignment problem (WAP), respectively     

Minimum-Energy Broadcasting in Static Ad Hoc Wireless Networks

Energy conservation is a critical issue in ad hoc wireless networks for node and network life, as the nodes are powered by batteries only. One major approach for energy conservation is to route a communication session along the route which requires the lowest total energy consumption. This optimization problem is referred to as Minimum-Energy Routing. While the minimum-energy unicast routing problem can be solved in polynomial time by shortest-path algorithms, it remains open whether the minimum-energy broadcast routing problem can be solved in polynomial time, despite the NP-hardness of its general graph version. Recently three greedy heuristics were proposed in [11]: MST (minimum spanning tree), SPT (shortest-path tree), and BIP (broadcasting incremental power). They have been evaluated through simulations in [11], but little is known about their analytical performances. The main contribution of this paper is a quantitative characterization of their performances in terms of approximation ratios. By exploring geometric structures of Euclidean MSTs, we have been able to prove that the approximation ratio of MST is between 6 and 12, and the approximation ratio of BIP is between 13/3 and 12. On the other hand, we show that the approximation ratio of SPT is at least n/2, where n is the number of receiving nodes. To the best of our knowledge, these are the first analytical results for the minimum-energy broadcasting problem.     

An iterative algorithm for delay-constrained minimum-costmulticasting

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     

Fast vicinity-upgrade algorithm for rectilinear Steiner trees

A new algorithm for rectilinear Steiner trees (RST) is presented. The proposed algorithm is based on successively constructing a vicinity structure from a rectilinear minimum spanning tree (MST) and generating a refined RST. The algorithm achieves an 8.5-10% average cost improvement over the rectilinear MST at a time complexity of O(n log n). To address specifically the linear programming approach of global routing the algorithm is modified to generate K trees.<>     

A rearrangeable algorithm for the construction of delay-constraineddynamic multicast trees

With the proliferation of multimedia group applications, the construction of multicast trees satisfying quality of service (QoS) requirements is becoming a problem of prime importance. Many of the multicast applications (such as video broadcasts and teleconferencing) require the network to support dynamic multicast sessions wherein the membership of the multicast group changes with time. In this paper, we propose and evaluate an algorithm called CRCDM (controlled rearrangement for constrained dynamic multicasting) for on-line update of multicast trees to adjust to changes in group membership. The CRCDM algorithm is based on a concept called quality factor (QF) that represents the usefulness of a portion of the multicast tree to the overall multicast session. When the usefulness of a particular region of the tree drops below a threshold, a rearrangement technique is used to suitably modify the tree. Our algorithm aims to satisfy the delay constraints of all current group members, at the same time minimizing the cost of the constructed tree. We compare the performance of our algorithm, by simulation, with that of an off-line Steiner heuristic; with ARIES, a previously published algorithm for on-line update of unconstrained trees; and with the algorithm proposed by Hong, Lee and Park (see Proc. IEEE INFOCOM, p.1433-40, 1998) for on-line update of delay-constrained trees. The simulation results indicate that our algorithm provides excellent cost-competitiveness that is better than that provided by the algorithm described by Hong et al., minimizes changes in the multicast tree after each update, and performs favorably even when compared with the unconstrained ARIES heuristic     

Video distribution on multicast networks

The Internet is being used to distribute video programming to small, widely distributed audiences over a multicast backbone (Mbone). This type of service can be used to deliver specialized programming to the general population. As the service becomes more widely used, conserving the required transmission facilities becomes more important. We define the problem of designing multicast networks for video distribution. The problem is related to the Steiner tree problem, with an interesting twist. The line costs are not constant. An heuristic is developed to solve the problem and the new heuristic is related to and compared with heuristics, developed for the Steiner tree problem and algorithms to design minimum depth and minimum spanning trees     

A heuristic for constructing a rectilinear Steiner tree by reusing routing resources over obstacles

The obstacle-avoiding rectilinear Steiner minimal tree (OARSMT) problem is a hot topic in very-large-scale integration physical design. In practice, most of the obstacles occupy the device layer and certain lower metal layers. Therefore, we can place wires on top of the obstacles. To maximize routing resources over obstacles, we propose a heuristic for constructing a rectilinear Steiner tree with slew constraints. Our algorithm adopts an extended rectilinear full Steiner tree grid as the routing graph. We mark two types of Steiner point candidates, which are used for constructing Steiner trees and refining solutions. A shortest path heuristic variant is designed for constructing Steiner trees and it takes into account slew constraint by inhibiting growth. Furthermore, we use a pre-computed strategy to avoid calculating slew rate repeatedly. Experimental results show that our algorithm maximizes routing resources over obstacles and saves routing resources outside obstacles. Compared with the conventional OARSMT algorithm, our algorithm reduces the wire length outside obstacles by as much as 18.74% and total wire length by as much as 6.03%. Our algorithm improves the latest related algorithm by approximately 2% in terms of wire length within a reasonable running time. Additionally, calculating the slew rate only accounts for approximately 15% of the total runing time.     

Tabu search based algorithms for bandwidth-delay-constrained least-cost multicast routing

The advent of various real-time multimedia applications in high-speed networks creates a need for quality of service (QoS) based multicast routing. The Steiner tree problem, is a well-known NP-complete problem, provides the mathematical structure behind multicast communications. Two important QoS constraints are the bandwidth constraint and the end-to-end delay constraint. In this paper, we propose various algorithms to solve the bandwidth-delay-constrained least-cost multicast routing problem based on Tabu Search (TS), addressing issues of the selected initial solution and move type as two major building blocks in short-term memory version of Tabu Search and longer-term memory with associated intensification and diversification strategies as advanced Tabu Search techniques. We evaluate the performance and efficiency of the proposed TS-based algorithms in comparison with other existing TS-based algorithms and heuristics on a variety of random generated networks with regard to total tree cost. Finally we identify the most efficient algorithm uncovered by our testing.     

加权的基于多播节点的多播路由算法

在许多多播应用中,降低多播树网络费用非常重要.本文提出了加权的基于多播节点的多播路由算法（WDDMC算法）.由于改变了DDMC（Destination-Driven routing for low-cost Multicast ）算法中的指示函数,适当降低了多播节点作为中间节点的优先级,提高非多播节点作为中间节点的优先级,从而使得多播树更接近最小Steiner树.在随机网络上的仿真结果表明,WDDMC算法的多播树网络费用优于DDMC算法.该算法的复杂度与DDMC算法完全相同.     

Maze Routing Steiner Trees With Delay Versus Wire Length Tradeoff

In this paper, we address the problem of generating good topologies of rectilinear Steiner trees using path search algorithms. Various techniques have been applied in order to achieve acceptable run times on a Maze Router that builds Steiner trees. A biasing technique proposed for wire length improvement, produces trees that are within 2% from optimal topologies in average. By introducing a sharing factor and a path-length factor we show how to trade-off wire length for delay. Experimental results show that our algorithm generates topologies with better delay compared to state of the art heuristics for Steiner trees, such as AHHK (from 26% to 40%) and P-Trees (from 1% to 30% and from 6% to 21% in the presence of blockages) while keeping the properties of a routing algorithm. An important motivation for this work lies in the fact that it can be used for estimation in the early stages as well as for actual routing, thereby improving the convergence and timing closure of the design significantly. We also provide some valuable theoretical background and insights on delay optimization and on how it relates to our maze router implementation.      

A Distributed Routing Method for Dynamic Multicasting

Single point, sender based control does not scale well for multicast delivery. For applications, such as group video or teleconferencing a low total cost multicast tree is required. In this article we present a destination driven algorithm to minimize the total tree cost of multicast tree in a dynamic situation for the whole session duration. In this heuristic approach we considered the staying duration of participants are available at the time of joining. The performance of our algorithm is analyzed through extensive simulation and evaluated against several other existing dynamic multicast routing and also against one well known near optimum heuristic algorithm used for solving Steiner tree problem. We have further tested our algorithm using erroneous information given by the joining participants. Simulation results show that its performance does not degrade that much even when the range of error is considerably high, which proves the robustness of our algorithm.