Node-disjoint Trees Research Articles

Delay-constrained survivable multicast routing problem on WDM networks for node failure case

With the rapid evolution of multimedia and real-time applications like audio/video conferencing, certain quality-of-service (QoS) should be guaranteed for the multicast transmission. For the given delay-constrained multicast request, the goal of delay-constrained survivable multicast routing problem (DCSMRP) is to provide the primary multicast tree and protecting resources so that after recovering from the link (node)-failure, the recovered tree can satisfy the delay constraint. In this article, the DCSMRP with a single node-failure case on wavelength-division multiplexing (WDM) networks is considered. Three node-failure protecting methods, includes node-disjoint trees (NDT), node-encircling p-cycles (NEPCs) and failure-independent path protecting p-cycles (FIPP p-cycles) are used in this article. For each protecting method, an algorithm is designed to solve the studied problem. Simulations are also conducted to evaluate the performance of the proposed algorithms.

Improved approximation for spanning star forest in dense graphs

A spanning subgraph of a graph G is called a spanning star forest of G if it is a collection of node-disjoint trees of depth at most 1. The size of a spanning star forest is the number of leaves in all its components. The goal of the spanning star forest problem is to find the maximum-size spanning star forest of a given graph. In this paper, we study the spanning star forest problem on c-dense graphs, where for any fixed c?(0,1), a graph of n vertices is called c-dense if it contains at least cn 2/2 edges. We design a $(\alpha+(1-\alpha)\sqrt{c}-\epsilon)$ -approximation algorithm for spanning star forest in c-dense graphs for any ?>0, where $\alpha=\frac{193}{240}$ is the best known approximation ratio of the spanning star forest problem in general graphs. Thus, our approximation ratio outperforms the best known bound for this problem when dealing with c-dense graphs. We also prove that, for any constant c?(0,1), approximating spanning star forest in c-dense graphs is APX-hard. We then demonstrate that for weighted versions (both node- and edge-weighted) of this problem, we cannot get any approximation algorithm with strictly better performance guarantee on c-dense graphs than on general graphs. Finally, we give strong inapproximability results for a closely related problem, namely the minimum dominating set problem, restricted on c-dense graphs.

Combining Tree Partitioning, Precedence, and Incomparability Constraints

The tree constraint partitions a directed graph into node-disjoint trees. In many practical applications that involve such a partition, there exist side constraints specifying requirements on tree count, node degrees, or precedences and incomparabilities within node subsets. We present a generalisation of the tree constraint that incorporates such side constraints. The key point of our approach is to take partially into account the strong interactions between the tree partitioning problem and all the side constraints, in order to avoid thrashing during search. We describe filtering rules for this extended tree constraint and evaluate its effectiveness on three applications: the Hamiltonian path problem, the ordered disjoint paths problem, and the phylogenetic supertree problem.