Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Competitive Analysis of Online Path Selection: Impacts of Path Length, Topology, and System-Level Costs

Ying Cao, Siyuan Yu, Xiaoqi Tan, Danny H. K. Tsang

TL;DR

This work addresses online path selection with self-interested users by employing competitive analysis to bound social welfare under worst-case arrivals. It introduces the posted-price mechanism PPM-PS$_{\phi}$ with exponential edge pricing $\phi_e^{\gamma}(\omega)=e^{\gamma\omega/C_e}-1$, and derives topology-dependent competitive guarantees for line and tree networks under path-length bounds $m \le |P_i| \le M$. Key results include line-network bounds $O\big(\max\{\ln M\bar{p}, \beta\ln(\frac{M\bar{p}}{2m\beta}+1)\}\big)$ and tree-network bounds under SR/EL patterns, with special cases recovering $O(\ln\frac{M\bar{p}}{m})$ in uniform-capacity scenarios; the work also integrates system-level costs via a differential-equation formulation on $\phi_e$ to preserve competitiveness. Extensive experiments corroborate the theory and reveal nuanced interactions between topology, path-length bounds, and price aggressiveness $\gamma$, offering practical guidance on network design and online algorithm selection under constrained adversaries.

Abstract

Consider a communication network to which a sequence of self-interested users come and send requests for data transmission between nodes. This work studies the question of how to guide the path selection choices made by those online-arriving users and maximize the social welfare. Competitive analysis is the main technical tool. Specifically, the impacts of path length bounds and topology on the competitive ratio of the designed algorithm are analyzed theoretically and explored experimentally. We observe intricate and interesting relationships between the empirical performance and the studied network parameters, which shed some light on how to design the network. We also investigate the influence of system-level costs on the optimal algorithm design.

Competitive Analysis of Online Path Selection: Impacts of Path Length, Topology, and System-Level Costs

TL;DR

This work addresses online path selection with self-interested users by employing competitive analysis to bound social welfare under worst-case arrivals. It introduces the posted-price mechanism PPM-PS with exponential edge pricing , and derives topology-dependent competitive guarantees for line and tree networks under path-length bounds . Key results include line-network bounds and tree-network bounds under SR/EL patterns, with special cases recovering in uniform-capacity scenarios; the work also integrates system-level costs via a differential-equation formulation on to preserve competitiveness. Extensive experiments corroborate the theory and reveal nuanced interactions between topology, path-length bounds, and price aggressiveness , offering practical guidance on network design and online algorithm selection under constrained adversaries.

Abstract

Consider a communication network to which a sequence of self-interested users come and send requests for data transmission between nodes. This work studies the question of how to guide the path selection choices made by those online-arriving users and maximize the social welfare. Competitive analysis is the main technical tool. Specifically, the impacts of path length bounds and topology on the competitive ratio of the designed algorithm are analyzed theoretically and explored experimentally. We observe intricate and interesting relationships between the empirical performance and the studied network parameters, which shed some light on how to design the network. We also investigate the influence of system-level costs on the optimal algorithm design.
Paper Structure (17 sections, 8 theorems, 23 equations, 8 figures, 1 algorithm)

This paper contains 17 sections, 8 theorems, 23 equations, 8 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Contributions and Paper Organization
  4. System Description and Results
  5. Posted-Price Mechanism
  6. Main Results I: Topology-Dependent Theoretical Guarantees of PPM-PS$_{\phi}$
  7. Line Network
  8. Tree Network
  9. Main Results II: Impact of System-Level Costs on Optimal Design of PPM-PS$_{\phi}$
  10. Experiments
  11. Description of Experiment Setting
  12. Experimental Findings and Discussions
  13. Impacts of Maximum Path Length
  14. Impacts of Minimum Path Length
  15. Hard Instances
  16. ...and 2 more sections

Key Result

Theorem 1

For line networks, when $\epsilon \le \frac{C_{\min}}{\gamma}$, PPM-PS$_{\phi}$ is $\max\{O(\ln M\bar{p}), O(\beta \ln (\frac{M\bar{p}}{2m \beta}+1))\}$-competitive, where $\beta$ is the ratio between the largest capacity and the smallest capacity in the network.

Figures (8)

  • Figure 1: Illustration of Network Topology
  • Figure 2: Impact of maximum path length $M$ in line networks. We conduct experiments for different values of $M$ while fixing the minimum path length $m$ at 1 for different values of $\gamma$: 0.5 (left), 2 (middle), and 4 (right). We plot the empirical ratio $\textsf{OPT}(I)/\textsf{ALG}(I)$, utilization statistics of edges in the network, and the acceptance rate of requests.
  • Figure 3: Impact of maximum path length $M$ in tree networks. The minimum path length $m$ is fixed at $1$ for different values of $\gamma$: 0.5 (left), 2 (middle), and 4 (right).
  • Figure 4: Impact of minimum path length $m$ in line networks. The maximum path length $M$ is fixed at $50$ for different values of $\gamma$: 0.5 (left), 2 (middle), and 4 (right).
  • Figure 5: Impacts of minimum path length $m$ in tree networks. The maximum path length $M$ is fixed at $8$ for different values of $\gamma$: 0.5 (left), 2 (middle), and 4 (right).
  • ...and 3 more figures

Theorems & Definitions (17)

  • Theorem 1
  • proof
  • Corollary 1
  • Corollary 2
  • Lemma 1
  • proof
  • Remark 1
  • Theorem 2
  • proof
  • Theorem 3
  • ...and 7 more