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 RPM’s efficiency in managing the network resources. The performance of one semiconstrained heuristic, MSC, three constrained Steiner tree (CST) heuristics, KPP, CAO, and BSMA, and one constrained shortest path tree (CSPT) 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. 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.

We study the problem of constructing multicast trees to meet the quality of service requirements of real-time, interactive applications operating in high-speed packet-switched environments. In particular, we assume that multicast communication depends on (a) bounded delay along the paths from the source to each destination, and (b) bounded variation among the delays along these paths. We first establish that the problem of determining such a constrained tree is NP-complete. We then derive heuristics that demonstrate good average case behavior in terms of the maximum inter-destination delay variation of the final tree. In addition, our heuristics achieve their best performance under conditions typical of multicast scenarios in high-speed networks. We also show that it is possible to dynamically reorganize the initial tree in response to changes in the destination set, in a way that is minimally disruptive to the multicast session. Department of Computer Science North Carolina State Uni...

We study the problem of finding small trees. Classical network design problems are considered with the additional constraint that only a specified number k of nodes are required to be connected in the solution. A prototypical example is the kMST problem in which we require a tree of minimum weight spanning at least k nodes in an edge-weighted graph. We show that the kMST problem is NP-hard even for points in the Euclidean plane. We provide approximation algorithms with performance ratio 2 p k for the general edge-weighted case and O(k 1=4 ) for the case of points in the plane. Polynomial-time exact solutions are also presented for the class of treewidth-bounded graphs which includes trees, series-parallel graphs, and bounded bandwidth graphs, and for points on the boundary of a convex region in the Euclidean plane. We also investigate the problem of finding short trees, and more generally, that of finding networks with minimum diameter. A simple technique is used to prov...

Efficient algorithms are known for computing a minimum spann.ing tree, or a shortest path. tree (with a fixed vertex as the root). The weight of a shortest path tree can be much more than the weight of a minimum spa,nning tree. Conversely, the distance bet,ween the root, and any vertex in a minimum spanning tree may be much more than the distance bet#ween the two vertices in the graph. Consider the problem of balancing between the two kinds of trees: Does every graph contain a tree that is “light ” (at most a constant times heavier than the minimum spanning t,ree), such that the distance from the root to any vertex in t,he tree is no more than a constant times the true distance? This paper answers the question in the affirmative. It is shown that there is a continuous tradeoff between the two parameters. For every y> 0, there is a tree in the graph whose total weight is at most 1 + $? times the weight of a minimum spanning tree, such that the di&nce in the tree between the root, and any vertex is at, most 1 + &y times the true distance. Efficient sequential and parallel algorithms achieving these factors are provided. The algorithms are shown to be optimal in two ways. First, it is shown that no algorithm can achieve better factors in all graphs, because there a.re graphs that do not have better trees. Second, it is shown that even on a per-graph basis, finding trees that achieve better factors is NP-hard.

In this paper we develop an optimal cache-oblivious priority queue data structure, supporting insertion, deletion, and deletemin operations in O ( 1 B logM/B N) amortized memory B transfers, where M and B are the memory and block transfer sizes of any two consecutive levels of a multilevel memory hierarchy. In a cache-oblivious data structure, M and B are not used in the description of the structure. The bounds match the bounds of several previously developed external-memory (cache-aware) priority queue data structures, which all rely crucially on knowledge about M and B. Priority queues are a critical component in many of the best known external-memory graph algorithms, and using our cache-oblivious priority queue we develop several cacheoblivious graph algorithms.

We present critical-sink routing tree (CSRT) constructions which exploit available critical-path information to yield high-performance routing trees. Our CS-Steiner and "Global Slack Removal" algorithms together modify traditional Steiner tree constructions to optimize signal delay at identified critical sinks. We further propose an iterative Elmore routing tree (ERT) construction which optimizes Elmore delay directly, as opposed to heuristically abstracting linear or Elmore delay as in previous approaches. Extensive timing simulations on industry IC and MCM interconnect parameters show that our methods yield trees that significantly improve (by averages of up to 67%) over minimum Steiner routings in terms of delays to identified critical sinks. ERTs also serve as generic high-performance routing trees when no critical sink is specified: for 8-sink nets in standard IC (MCM) technology, we improve average sink delay by 19% (62%) and maximum sink delay by 22% (52%) over the mini...

We study network-design problems with multiple design objectives. In particular, we look at two cost measures to be minimized simultaneously: the total cost of the network and the maximum degree of any node in the network. Our main result can be roughly stated as follows: given an integer b, we present approximation algorithms for a variety of network-design problems on an n- node graph in which the degree of the output network is O(b log( n b )) and the cost of this network is O(log n) times that of the minimum-cost degree-b-bounded network. These algorithms can handle costs on nodes as well as edges. Moreover, we can construct such networks so as to satisfy a variety of connectivity specifications including spanning trees, Steiner trees and generalized Steiner forests. The performance guarantee on the cost of the output network is nearly best-possible unless NP = ~ P . We also address the special case in which the costs obey the triangle inequality. In this case, we obtai...

A new heuristic algorithm is presented for constructing minimum-cost multicast trees with delay constraints. The new algorithm can set variable delay bounds on destinations and handles two variants of the network cost optimization goal: one minimizing the total cost (total bandwidth utilization) of the tree, and another minimizing the maximal link cost (the most congested link). Instead of the single-pass tree construction approach used in most previous heuristics, the new algorithm is based on a feasible search optimization method which starts with the minimumdelay tree and monotonically decreases the cost by iterative improvement of the delay-bounded tree. The optimality of the costs of the delay-bounded trees obtained with the new algorithm is analyzed by simulation. Depending on how tight the delay bounds are, the costs of the multicast trees obtained with the new algorithm are shown to be very close to the costs of the trees obtained by the Kou, Markowsky and Berman's algorithm. ...

We consider the survivable network design problem-- the problem of designing, at minimum cost, a network with edge-connectivity requirements. As special cases, this problem encompasses the Steiner tree problem, the traveling salesman problem and the k-edge-connected network design problem. We establish a property, referred to as the parsimonious property, of the linear programming (LP) relaxation of a classical formulation for the problem. The parsimonious property has numerous consequences. For example, we derive various structural properties of these LP relaxations, we present some algorithmic improvements and we perform tight worst-case analyses of two heuristics for the survivable network design problem.

There is a growing demand for network devices capable of examining the content of data packets in order to improve network security and provide application-specific services. Most high performance systems that perform deep packet inspection implement simple string matching algorithms to match packets against a large, but finite set of strings. However, there is growing interest in the use of regular expression-based pattern matching, since regular expressions offer superior expressive power and flexibility. Deterministic finite automata (DFA) representations are typically used to implement regular expressions. However, DFA representations of regular expression sets arising in network applications require large amounts of memory, limiting their practical application. In this paper, we introduce a new representation for regular