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

## TL;DR

This paper introduces polynomial heuristic algorithms to approximate solutions for a complex NP-hard problem involving energy-efficient, bounded-hop communication trees in Euclidean networks, with comparative analysis of their performance.

## Contribution

It presents new heuristic algorithms for the Min-Power Bounded-Hops Symmetric Connectivity problem in Euclidean networks, addressing its NP-hardness.

## Key findings

- Heuristic algorithms achieve near-optimal solutions.
- Comparative analysis demonstrates effectiveness of proposed methods.
- Results show trade-offs between power consumption and hop bounds.

## Abstract

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.