[Paper Review] Data Delivery by Mobile Agents with Energy Constraints over a fixed path

Aristotelis Giannakos, Mhand Hifi+1 more|arXiv (Cornell University)|Mar 16, 2017

Optimization and Search Problems4 references3 citations

TL;DR

This paper presents a 3-approximation polynomial-time algorithm for the Min-Range Uniform Data Delivery over a Path (min-RIPDD) problem, where k mobile agents with identical energy budgets must deliver data from source s to target t along a fixed path. The algorithm uses a matching-based strategy over strategically placed selection points to minimize the required energy budget, ensuring efficient data handovers with at most one transfer per agent.

ABSTRACT

We consider $k$ mobile agents of limited energy that are initially located at vertices of an edge-weighted graph $G$ and have to collectively deliver data from a source vertex $s$ to a target vertex $t$. The data are to be collected by an agent reaching $s$, who can carry and then hand them over another agent etc., until some agent with the data reaches $t$. The data can be carried only over a fixed $s-t$ path of $G$; each agent has an initial energy budget and each time it passes an edge, it consumes the edge's weights in energy units and stalls if its energy is not anymore sufficient to move. The main result of this paper is a 3-approximation polynomial time algorithm for the data delivery problem over a fixed $s-t$ path in the graph, for identical initial energy budgets and at most one allowed data hand-over per agent.

Motivation & Objective

• To address the challenge of delivering data from a source to a target using mobile agents with limited energy budgets.
• To minimize the required initial energy budget for data delivery over a fixed path in a graph.
• To design a polynomial-time approximation algorithm for the NP-hard min-RIPDD problem with identical agent energy budgets and at most one data handover per agent.
• To improve upon greedy approaches by using a matching-based strategy between agents and selection points on the path.
• To provide a provably bounded approximation algorithm for energy-aware mobile agent data delivery.

Proposed method

• The algorithm constructs a set of selection points along the fixed s-t path at intervals determined by a parameter β, where β ranges from W/k to W.
• It forms a complete weighted bipartite graph between agents and selection points, with edge weights representing shortest path distances from agents to selection points.
• A minimum-maximum-weight maximal matching is computed for each β to assign agents optimally to selection points.
• The algorithm evaluates all such β values and returns the best solution among all β-based matchings.
• The final solution is derived by combining the matching strategy with a greedy selection of agents to fetch data at each selection point, ensuring energy constraints are respected.
• Theoretical analysis proves that the algorithm achieves a 3-approximation ratio by bounding the optimal solution using distance and path segment constraints.

Experimental results

Research questions

• RQ1 Can a polynomial-time approximation algorithm be designed for the min-RIPDD problem with identical energy budgets and single data handovers?
• RQ2 What is the best possible approximation ratio achievable for this data delivery problem under energy constraints?
• RQ3 How can agent-to-selection-point assignment be optimized to reduce the required energy budget?
• RQ4 Does a matching-based approach outperform greedy selection in terms of approximation ratio?
• RQ5 Can the problem be solved efficiently even when agents must traverse non-direct paths to reach selection points?

Key findings

• The proposed Matching β algorithm achieves a 3-approximation ratio for the min-RIPDD problem, proving that the solution’s energy requirement is at most three times the optimal.
• The algorithm guarantees a constant approximation ratio by leveraging Dirichlet’s box principle to ensure coverage of optimal selection points across path segments.
• The analysis shows that the optimal solution’s energy budget R* satisfies R* ≥ d* and R* ≥ b*, where d* is the maximum agent-to-selection-point distance and b* is the maximum path segment length in the optimal solution.
• The algorithm’s performance is bounded by R ≤ d_b + b*, where d_b is the maximum distance in the matching solution and b* is the optimal segment length, leading to 3R* ≥ R.
• The algorithm outperforms greedy approaches by using a global matching strategy instead of local, short-sighted agent selection.
• The result holds even when agents must take detours to reach selection points, as long as they have sufficient energy to traverse the shortest path.