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The Power of Alternatives in Network Embedding

Oleg Kolosov, Gala Yadgar, David Breitgand, Dean H. Lorenz

TL;DR

This paper introduces Virtual Network Embedding with Alternatives (VNEAP), a novel generalization of the classic Virtual Network Embedding Problem that allows each application request to be embedded using one of multiple topology alternatives. It develops two scalable heuristics, GREEDY and TANTo, where TANTo employs aggregation and LP relaxation to yield near-optimal solutions with a provable bound on the cost-rejection gap. Through large-scale simulations on diverse edge-to-cloud topologies and realistic CCTV-inspired workloads, the study demonstrates that enabling topology alternatives substantially improves cost efficiency and substrate utilization, with TANTo achieving near-optimal performance and substantial runtime benefits from parallelization. The work highlights the practical value of modeling alternative configurations in network virtualization and lays groundwork for future extensions to energy minimization, latency constraints, online deployments, and general-graph topologies via tree decompositions.

Abstract

In the virtual network embedding problem, the goal is to map embed a set of virtual network instances to a given physical network substrate at minimal cost, while respecting the capacity constraints of the physical network. This NP-hard problem is fundamental to network virtualization, embodying essential properties of resource allocation problems faced by service providers in the edge-to-cloud spectrum. Due to its centrality, this problem and its variants have been extensively studied and remain in the focus of the research community. In this paper, we present a new variant, the virtual network embedding with alternatives problem (VNEAP). This new problem captures the power of a common network virtualization practice, in which virtual network topologies are malleable - embedding of a given virtual network instance can be performed using any of the alternatives from a given set of topology alternatives. We provide two efficient heuristics for VNEAP and show that having multiple virtual network alternatives for the same application is superior to the best results known for the classic formulation. We conclude that capturing the problem domain via VNEAP can facilitate more efficient network virtualization solutions.

The Power of Alternatives in Network Embedding

TL;DR

This paper introduces Virtual Network Embedding with Alternatives (VNEAP), a novel generalization of the classic Virtual Network Embedding Problem that allows each application request to be embedded using one of multiple topology alternatives. It develops two scalable heuristics, GREEDY and TANTo, where TANTo employs aggregation and LP relaxation to yield near-optimal solutions with a provable bound on the cost-rejection gap. Through large-scale simulations on diverse edge-to-cloud topologies and realistic CCTV-inspired workloads, the study demonstrates that enabling topology alternatives substantially improves cost efficiency and substrate utilization, with TANTo achieving near-optimal performance and substantial runtime benefits from parallelization. The work highlights the practical value of modeling alternative configurations in network virtualization and lays groundwork for future extensions to energy minimization, latency constraints, online deployments, and general-graph topologies via tree decompositions.

Abstract

In the virtual network embedding problem, the goal is to map embed a set of virtual network instances to a given physical network substrate at minimal cost, while respecting the capacity constraints of the physical network. This NP-hard problem is fundamental to network virtualization, embodying essential properties of resource allocation problems faced by service providers in the edge-to-cloud spectrum. Due to its centrality, this problem and its variants have been extensively studied and remain in the focus of the research community. In this paper, we present a new variant, the virtual network embedding with alternatives problem (VNEAP). This new problem captures the power of a common network virtualization practice, in which virtual network topologies are malleable - embedding of a given virtual network instance can be performed using any of the alternatives from a given set of topology alternatives. We provide two efficient heuristics for VNEAP and show that having multiple virtual network alternatives for the same application is superior to the best results known for the classic formulation. We conclude that capturing the problem domain via VNEAP can facilitate more efficient network virtualization solutions.
Paper Structure (17 sections, 4 theorems, 5 equations, 12 figures, 3 tables, 3 algorithms)

This paper contains 17 sections, 4 theorems, 5 equations, 12 figures, 3 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. A Simple Example
  4. Virtual Network Embedding with Alternatives Problem
  5. Definitions and Notations Common to vneap and vnep
  6. Definitions and Notations Unique to vneap
  7. Problem Statement
  8. Solving \ref{['prob:vnea']}
  9. GREEDY Algorithm
  10. TANTO Algorithm
  11. Aggregation and Relaxation
  12. Rounding and Embedding of Individual Requests
  13. Analysis
  14. Evaluation
  15. Experimental Setup
  16. ...and 2 more sections

Key Result

Lemma 1

The cost of rejection added by tanto is bounded by $\Psi(\IfNoValueTF{-NoValue-} {\boldsymbol{x}} {\boldsymbol{x}_{-NoValue-}}^{\textsc{t\tiny\!anto}}) -\Psi(\IfNoValueTF{-NoValue-} {\boldsymbol{\tilde{x}}} {\boldsymbol{\tilde{x}}_{-NoValue-}}^{\textsc{v{\tiny\!neap}l\tiny{p}}}) \le \psi d(r)^{\max}

Figures (12)

  • Figure 1: Alternative topologies
  • Figure 2: Substrate topology
  • Figure 3: Embedding with alternatives
  • Figure 4: MILP formulation for vneap
  • Figure 5: CCTV virtual network. The numbers indicate function and link sizes.
  • ...and 7 more figures

Theorems & Definitions (4)

  • Lemma 1
  • Theorem 1
  • Lemma 2
  • Theorem 2