[Paper Review] Problem Complexity in Parallel Problem Solving

Sebastian Herrmann, Jörn Grahl+1 more|arXiv (Cornell University)|Mar 25, 2014

Computability, Logic, AI Algorithms18 references3 citations

TL;DR

This paper investigates how problem complexity moderates the impact of communication network structure on group performance in parallel problem solving. Using multi-agent simulations on NK-landscapes and TSP instances, it finds that network topology significantly affects success only at moderate problem complexity, with influence diminishing for very easy or very hard problems—resolving apparent contradictions in prior literature.

ABSTRACT

Recent works examine the relationship between the communication structure and the performance of a group in a problem solving task. Some conclude that inefficient communication networks with long paths outperform efficient networks on the long run. Others find no influence of the network topology on group performance. We contribute to this discussion by examining the role of problem complexity. In particular, we study whether and how the complexity of the problem at hand moderates the influence of the communication network on group performance. Results obtained from multi-agent modelling suggest that problem complexity indeed has an influence. We observe an influence of the network only for problems of moderate difficulty. For easier or harder problems, the influence of network topology becomes weaker or irrelevant, which offers a possible explanation for inconsistencies in the literature.

Motivation & Objective

• To resolve conflicting findings in the literature regarding whether efficient or inefficient communication networks outperform in group problem solving.
• To investigate whether problem complexity acts as a moderating factor in the relationship between network structure and group performance.
• To test whether the influence of network topology on group success varies with the difficulty of the problem being solved.
• To determine if the observed differences in network performance across studies are due to variations in task complexity.
• To provide empirical evidence from multi-agent modeling that network effects are not universally applicable but depend on problem difficulty.

Proposed method

• Modified the Lazer & Friedman (LF) agent-based model to vary problem complexity using the NK-landscape model, where K controls interdependencies between binary decision variables.
• Generated 100 random NK-landscapes for each K ∈ [0, 19] with N = 20 bits to test a range of problem complexities.
• Simulated group problem solving on two network topologies: linear (long path lengths) and totally connected (short path lengths).
• Measured group performance as the probability that at least one agent found the global optimum across 100 repetitions per landscape.
• Reproduced results using the Traveling Salesman Problem (TSP) with varying numbers of cities to test robustness beyond the NK-landscape.
• Defined network influence as the difference in success probabilities between the linear and totally connected networks across complexity levels.

Experimental results

Research questions

• RQ1 Does problem complexity moderate the influence of communication network structure on group performance in parallel problem solving?
• RQ2 For which levels of problem complexity is network topology most influential in determining group success?
• RQ3 Are the conflicting results in prior studies (e.g., Lazer & Friedman vs. Mason & Watts) explainable by differences in task complexity?
• RQ4 Is the observed network effect specific to the NK-landscape model, or does it generalize to other problem types like the TSP?
• RQ5 Does the relationship between network structure and performance follow a curvilinear pattern across the complexity spectrum?

Key findings

• Network structure significantly influences group performance only at moderate problem complexity, as measured by the K parameter in the NK-landscape.
• For K = 0 (very easy problems), the difference in success probability between linear and totally connected networks is negligible, indicating no meaningful network effect.
• For K = 19 (very hard problems), the network influence also diminishes, with both network types showing low and similar success rates.
• The peak network influence occurs at intermediate K values, where the linear network outperforms the totally connected network in long-run success probability.
• The curvilinear relationship between problem complexity and network influence is replicated in the TSP, confirming it is not an artifact of the NK-landscape model.
• The findings suggest that inconsistent results in prior studies may stem from tasks being too easy or too hard for network structure to have a detectable effect.