Constructive Heuristics for Min-Power Bounded-Hops Symmetric Connectivity Problem

We consider a Min-Power Bounded-Hops Symmetric Connectivity problem that consists in the construction of communication spanning tree on a given graph, where the total energy consumption spent for the data transmission is minimized and the maximum number of hops between two nodes is bounded by some predefined constant. We focus on the planar Euclidian case of this problem where the nodes are placed at the random uniformly spread points on a square and the power cost necessary for the communication between two network elements is proportional to the squared distance between them. Since this is an NP-hard problem, we propose different polynomial heuristic algorithms for the approximation solution to this problem. We perform a posteriori comparative analysis of the proposed algorithms and present the obtained results in this paper

Metaheuristics for Min-Power Bounded-Hops Symmetric Connectivity Problem

We consider a Min-Power Bounded-Hops Symmetric Connectivity problem that consists of the construction of communication spanning tree on a given graph, where the total energy consumption spent for the data transmission is minimized and the maximum number of edges between two nodes is bounded by some predefined constant. We focus on the planar Euclidian case of this problem where the nodes are placed at the random uniformly spread points on a square and the power cost necessary for the communication between two network elements is proportional to the squared distance between them. Since this is an NP-hard problem, we propose different heuristics based on the following metaheuristics: genetic local search, variable neighborhood search, and ant colony optimization. We perform a posteriori comparative analysis of the proposed algorithms and present the obtained results in this paper.Comment: arXiv admin note: text overlap with arXiv:1902.0679

Parameterized Algorithms for Power-Efficiently Connecting Wireless Sensor Networks: Theory and Experiments

We study an NP-hard problem motivated by energy-efficiently maintaining the connectivity of a symmetric wireless communication network: Given an edge-weighted $n$-vertex graph, find a connected spanning subgraph of minimum cost, where the cost is determined by letting each vertex pay the most expensive edge incident to it in the subgraph. On the negative side, we show that $o(\log n)$-approximating the difference $d$ between the optimal solution cost and a natural lower bound is NP-hard and that, under the Exponential Time Hypothesis, there are no exact algorithms running in $2^{o(n)}$ time or in $f(d)\cdot n^{O(1)}$ time for any computable function $f$. Moreover, we show that the special case of connecting $c$ network components with minimum additional cost generally cannot be polynomial-time reduced to instances of size $c^{O(1)}$ unless the polynomial-time hierarchy collapses. On the positive side, we provide an algorithm that reconnects $O(\log n)$ connected components with minimum additional cost in polynomial time. These algorithms are motivated by application scenarios of monitoring areas or where an existing sensor network may fall apart into several connected components due to sensor faults. In experiments, the algorithm outperforms CPLEX with known ILP formulations when $n$ is sufficiently large compared to $c$.Comment: Additional experiments, lower bounds strengthened to metric case, added kernelization lower bound