Constrained Steiner Tree Problem Research Articles

A Lagrangean-based decomposition approach for the link constrained Steiner tree problem

The link constrained Steiner tree problem is a variant of the classic Steiner tree problem where the number of links to be activated must not exceed a pre-fixed value. We introduce a multi-start heuristic to obtain a quick feasible solution. The proposed heuristic is embedded into a decomposition framework based on Lagrangean relaxation. In particular, the relaxed problem is decomposed into two polynomially solvable subproblems and, to tackle the Lagrangean dual, we introduce a dual ascent procedure where just one multiplier at a time is updated. Our approach can be classified as a Lagrangean heuristic. In fact, at each iteration of the dual ascent procedure, the information derived from the solution of the relaxed problem is used to provide a feasible solution, by solving a restricted problem defined on an appropriate subgraph. Several versions of the proposed approach are defined and tested on instances drawn from the scientific literature.

Hop constrained Steiner trees with multiple root nodes

We consider a network design problem that generalizes the hop and diameter constrained Steiner tree problem as follows: Given an edge-weighted undirected graph with two disjoint subsets representing roots and terminals, find a minimum-weight subtree that spans all the roots and terminals so that the number of hops between each relevant node and an arbitrary root does not exceed a given hop limit H. The set of relevant nodes may be equal to the set of terminals, or to the union of terminals and root nodes. This article proposes integer linear programming models utilizing one layered graph for each root node. Different possibilities to relate solutions on each of the layered graphs as well as additional strengthening inequalities are then discussed. Furthermore, theoretical comparisons between these models and to previously proposed flow- and path-based formulations are given. To solve the problem to optimality, we implement branch-and-cut algorithms for the layered graph formulations. Our computational study shows their clear advantages over previously existing approaches.

Niched ant colony optimization with colony guides for QoS multicast routing

Quality-of-service (QoS) multicast routing is essential to many network applications such as IPTV, Internet radio, multimedia broadcasting, and real-time telecommunication. Recently, the minimum-cost multicast tree with the delay-and-bandwidth constraint (MinC/DB) problem in QoS multicast routing has caused the most attention. As the MinC/DB problem can be reduced to the constrained Steiner tree problem which has been shown to be NP-complete, it is very unlikely that a polynomial time algorithm would exist. In this paper, we propose a niched ant colony optimization with colony guides (NACOg) algorithm to tackle the MinC/DB problem. The NACOg algorithm first deliberates a constrained tree traversal (CTT) strategy that guarantees the search to any feasible trees with respect to the QoS constraints. The proposed CTT strategy employs adaptive memory structure as contemplated in the tabu search and the strategy is more effective in constraint-handling than both the penalty-function and the produce-and-repair strategies which were broadly used in the literature. The evolutionary optimization of the NACOg algorithm is empowered by the search balance between diversification and intensification. The diversification search is practiced by the individual niche-colony with its own pheromone matrix, and the intensification search is facilitated by the learning scheme which refers to the experience obtained by the niche-colony guide and the entire-colony guide. The experimental results on 100 problem instances have shown that the proposed NACOg algorithm produces the least cost QoS multicast trees compared to those obtained by the Haghighat genetic algorithm and the well-known KPP heuristic.

A hybrid scatter search meta-heuristic for delay-constrained multicast routing problems

This paper investigates the first hybrid scatter search and path relinking meta-heuristic for the Delay-Constrained Least-Cost (DCLC) multicast routing problem. The underpinning mathematic model of the DCLC multicast routing problem is the constrained Steiner tree problem in graphs, a well known NP-complete problem. After combining a path relinking method as the solution combination method in scatter search, we further explore two improvement strategies: tabu search and variable neighborhood search, to intensify the search in the hybrid scatter search algorithm. A large number of simulations on some benchmark instances from the OR-library and a group of random graphs of different characteristics demonstrate that the improvement strategy greatly affects the performance of the proposed scatter search algorithm. The hybrid scatter search algorithm intensified by a variable neighborhood descent search is highly efficient in solving the DCLC multicast routing problem in comparison with other algorithms and heuristics in the literature.

Multicast routing for delay variation bound using a modified ant colony algorithm

The delay and delay variation-bounded Steiner tree problem is an important multicast routing problem in real-time multimedia networks. Such a constrained Steiner tree problem is known to be NP-complete. This paper proposes an ant colony algorithm with orientation factor and applies it to multicast routing problem with the constraints of delay variation bound. The orientation factor enables the ant to get rid of the initial blindness when searching paths, makes use of the search results and reduces the misguiding effect of pheromone on irrelevant paths, thus overcoming the drawbacks of slow convergence existing in the basic ant colony algorithm, increasing the speed of convergence and speeding up the finding of feasible solution to the problem. The simulation results show that the modified algorithm makes it possible to find a feasible solution to the multicast routing problem with delay variation bound. Compared with the conventional ant colony algorithm, the convergence speed of the modified algorithm is improved.

Distributed multicast routing for delay and delay variation-bounded Steiner tree using simulated annealing

The delay and delay variation-bounded Steiner tree problem is an important multicast routing issue in real-time multimedia networks. Such a constrained Steiner tree problem is known to be NP-complete. In this paper, we propose a distributed multicast routing algorithm based on simulated annealing to produce routing trees having a minimal network cost under delay and delay variation constraints. The proposed algorithm is fully distributed, and supports the dynamic reorganizing of the multicast tree in response to changes for the destination. Simulations demonstrate that our algorithm is better in terms of tree cost as compared with other existing algorithms, and it performs excellently in delay and delay variation. Furthermore, it has high success ratio, rapid convergence and better real-time property.

Algorithms for delay-constrained low-cost multicast tree construction

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. Multicast groups are usually classified as sparse or pervasive groups depending on the physical distribution of group members. They are also classified based on the temporal characteristics of group membership into static and dynamic groups. In this paper, we propose two algorithms for constructing multicast trees for multimedia group communication in which the members are sparse and static. The proposed algorithms use a constrained distributed unicast routing algorithm for generating low-cost, bandwidth and delay constrained multicast trees. These algorithms have lower message complexity and call setup time due to their nature of iteratively adding paths, rather than edges, to partially constructed trees. We study the performance (in terms of call acceptance rate, call setup time and multicast tree cost) of these algorithms through simulation by comparing them with that of a recently proposed algorithm (V. Kompella, J.C. Pasquale, G.C. Polyzos, Two distributed algorithms for the constrained Steiner tree problem, in: Proc. Comp. Comm. Networking, San Diego, CA, June 1993) for the same problem. The simulation results indicate that the proposed algorithms provide larger call acceptance rates, lower setup times and comparable tree costs.

A constrained Steiner tree problem

The Steiner tree problem on a graph involves finding a minimum cost tree which connects a designated subset of the nodes in the graph. Variants of the basic Steiner tree model can arise in the design of telecommunication networks where customers must be connected to a switching center. In this paper, we consider the constrained Steiner tree problem which is the Steiner tree problem on graph with one additional side constraint that imposes a budget on the total amount of a resource (e.g., employee maintenance time) required by the arcs in the solution. We discuss various problem formulations, decomposition based solution approaches, and computational experience with the proposed methods.