SIAM Journal on Computing
A new approximation algorithm for the Steiner tree problem with performance ratio 5/3
Journal of Algorithms
Power consumption in packet radio networks
Theoretical Computer Science
On the Complexity of Computing Minimum Energy Consumption Broadcast Subgraphs
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
Symmetric Connectivity with Minimum Power Consumption in Radio Networks
TCS '02 Proceedings of the IFIP 17th World Computer Congress - TC1 Stream / 2nd IFIP International Conference on Theoretical Computer Science: Foundations of Information Technology in the Era of Networking and Mobile Computing
Power optimization for connectivity problems
Mathematical Programming: Series A and B
Power optimization in fault-tolerant topology control algorithms for wireless multi-hop networks
IEEE/ACM Transactions on Networking (TON)
Wireless network design via 3-decompositions
Information Processing Letters
An improved LP-based approximation for steiner tree
Proceedings of the forty-second ACM symposium on Theory of computing
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Survivable network activation problems
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
| Hi-index | 0.00 |
In the classical (min-cost) Steiner tree problem, we are given an edge-weighted undirected graph and a set of terminal nodes. The goal is to compute a min-cost tree S which spans all terminals. In this paper we consider the min-power version of the problem (a.k.a. symmetric multicast), which is better suited for wireless applications. Here, the goal is to minimize the total power consumption of nodes, where the power of a node v is the maximum cost of any edge of S incident to v. Intuitively, nodes are antennas (part of which are terminals that we need to connect) and edge costs define the power to connect their endpoints via bidirectional links (so as to support protocols with ack messages). Observe that we do not require that edge costs reflect Euclidean distances between nodes: this way we can model obstacles, limited transmitting power, non-omnidirectional antennas etc. Differently from its min-cost counterpart, min-power Steiner tree is NP-hard even in the spanning tree case (a.k.a. symmetric connectivity), i.e. when all nodes are terminals. Since the power of any tree is within once and twice its cost, computing a ρst≤ln (4)+ε [Byrka et al.'10] approximate min-cost Steiner tree provides a 2ρstε with a non-trivial approach in [Althaus et al.'06]. In this paper we present an improved approximation algorithm for min-power Steiner tree. Our result is based on two main ingredients. We present the first decomposition theorem for min-power Steiner tree, in the spirit of analogous structural results for min-cost Steiner tree and min-power spanning tree. Based on this theorem, we define a proper LP relaxation, that we exploit within the iterative randomized rounding framework in [Byrka et al.'10]. A careful analysis of the decrease of the power of nodes at each iteration provides a $3\ln 4-\frac{9}{4}+\varepsilon ε approximation for min-power spanning tree as well. This matches the approximation factor in [Nutov and Yaroshevitch'09] for the special case of min-power spanning tree with edge weights in {0,1}.