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Profit Maximization in Closed Social Networks

Poonam Sharma, Suman Banerjee

TL;DR

This work investigates Profit Maximization in Closed Social Networks (PMCSN), where diffusion is constrained to at most $\ell$ outgoing links per node and seed choices must respect a budget $B$. It formalizes the problem on a directed weighted graph with a diffusion network $G_D$, defines seed costs $C(u)$ and node benefits $b(u)$, and targets the profit $\phi(S) = \beta(S) - C(S)$ under the Independent Cascade-style diffusion. To address PMCSN, the paper introduces a sampling-based approximate approach and a marginal-gain–based heuristic (HEU), with detailed complexity and sample-bound analyses. Experiments on real-world datasets demonstrate that the proposed methods achieve higher profit than baselines, and the authors provide a public GitHub repository for replication.

Abstract

Diffusion of information, innovation, and ideas is an important phenomenon in social networks. Information propagates through the network and reaches from one person to the next. In many settings, it is meaningful to restrict diffusion so that each node can spread information to only a limited number of its neighbors rather than to all of them. Such social networks are called closed social networks. In recent years, social media platforms have emerged as an effective medium for commercial entities, where the objective is to maximize profit. In this paper, we study the Profit Maximization in Closed Social Networks (PMCSN) problem in the context of viral marketing. The input to the problem is a closed social network and two positive integers $\ell$ and $B$. The problem asks to select seed nodes within a given budget $B$; during the diffusion process, each node is restricted to choose at most $\ell$ outgoing links for information diffusion; and the objective is to maximize the profit earned by the seed set. The PMCSN problem generalizes the Influence Maximization problem, which is NP-hard. We propose two solution approaches for PMCSN: a sampling-based approximate solution and a marginal-gain-based heuristic solution. We analyze the sample complexity, running time, and space requirements of the proposed approaches. We conduct experiments on real-world, publicly available social network datasets. The results show that the seed sets and diffusion links chosen by our methods yield higher profit than baseline methods. The implementation and data are available at \texttt{https://github.com/PoonamSharma-PY/ClosedNetwork}.

Profit Maximization in Closed Social Networks

TL;DR

This work investigates Profit Maximization in Closed Social Networks (PMCSN), where diffusion is constrained to at most outgoing links per node and seed choices must respect a budget . It formalizes the problem on a directed weighted graph with a diffusion network , defines seed costs and node benefits , and targets the profit under the Independent Cascade-style diffusion. To address PMCSN, the paper introduces a sampling-based approximate approach and a marginal-gain–based heuristic (HEU), with detailed complexity and sample-bound analyses. Experiments on real-world datasets demonstrate that the proposed methods achieve higher profit than baselines, and the authors provide a public GitHub repository for replication.

Abstract

Diffusion of information, innovation, and ideas is an important phenomenon in social networks. Information propagates through the network and reaches from one person to the next. In many settings, it is meaningful to restrict diffusion so that each node can spread information to only a limited number of its neighbors rather than to all of them. Such social networks are called closed social networks. In recent years, social media platforms have emerged as an effective medium for commercial entities, where the objective is to maximize profit. In this paper, we study the Profit Maximization in Closed Social Networks (PMCSN) problem in the context of viral marketing. The input to the problem is a closed social network and two positive integers and . The problem asks to select seed nodes within a given budget ; during the diffusion process, each node is restricted to choose at most outgoing links for information diffusion; and the objective is to maximize the profit earned by the seed set. The PMCSN problem generalizes the Influence Maximization problem, which is NP-hard. We propose two solution approaches for PMCSN: a sampling-based approximate solution and a marginal-gain-based heuristic solution. We analyze the sample complexity, running time, and space requirements of the proposed approaches. We conduct experiments on real-world, publicly available social network datasets. The results show that the seed sets and diffusion links chosen by our methods yield higher profit than baseline methods. The implementation and data are available at \texttt{https://github.com/PoonamSharma-PY/ClosedNetwork}.
Paper Structure (18 sections, 3 theorems, 5 equations, 2 figures, 1 table, 2 algorithms)

This paper contains 18 sections, 3 theorems, 5 equations, 2 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. Background and Problem Definition
  3. (Closed) Social Networks
  4. Diffusion in Social Networks
  5. Profit Maximization in Social Networks
  6. Proposed Solution Approach
  7. Sampling-Based Approach
  8. Complexity Analysis
  9. Sample Bound Estimation
  10. Marginal Gain Based Heuristic (HEU) Solution
  11. Experimental Evaluation
  12. Dataset Description
  13. Experimental Setup and and Goals
  14. Experimental Results and Discussions
  15. Impact of Budget
  16. ...and 3 more sections

Key Result

theorem thmcountertheorem

In the worst case, the time and space requirements of the sampling-based approach will be of $\mathcal{O}(\frac{B}{C_{min}} \cdot (m+n) \cdot x)$ and $\mathcal{O}(x \cdot (m+n))$, respectively, where $x$ is the sample size.

Figures (2)

  • Figure 1: Budget Vs. Profit Earned Plots for Euemail ((a)-(h)) and Facebook ((i)-(p)) Dataset
  • Figure 2: Plots for Execution Time (in Seconds) taken by all Algorithms under various Budgets for Euemail ((a)-(h)) and Facebook ((i)-(p)) Dataset

Theorems & Definitions (9)

  • definition thmcounterdefinition: Diffusion Network
  • definition thmcounterdefinition: Independent Cascade Model
  • definition thmcounterdefinition: Influence of a Seed Set
  • definition thmcounterdefinition: Benefit earned by the Seed Set
  • definition thmcounterdefinition: Profit earned by the Seed Set
  • definition thmcounterdefinition: Profit Maximization in Closed Social Network (PMCSN Problem)
  • theorem thmcountertheorem
  • theorem thmcountertheorem
  • theorem thmcountertheorem