Implement `sequence.py` to find dyadic conversation sequence

[aridyckovsky]

Summary

A complete generate.py in #2 requires that the generated topology satisfies a sufficiency condition: it must permit r rounds of interaction to take place between dyads given experimental constraints, i.e., a valid sequence of interactions between participant nodes relative to its config.yml.

Motivation

This relates to the following milestones:

• Custom assignment to small world networks
• Generated sequence of chats per game
• YAML-spec treatment configurations

Completing this will also get us closer to #2 being complete.

Implementation

The below implementation is still missing a mechanism to dictate how many matchings a node must be a part of. It finds a sequence of rounds = 3 matchings:

import random
from itertools import chain
rounds = 3
dyads = [(u,v) for (u,v) in graph.edges]
interaction_sequence = []
tries = 5000

# This is 8 for n = 16
ideal_matching_size = round(len(graph.nodes()) / 2)
tries_since_ideal_matching = 0

print(f"Total available dyads: {len(dyads)}")

while tries:
    
    matching = set()
    matching.add(random.choice(dyads))

    nodes_in_matching = set(chain(*matching))

    for dyad in dyads:
        u,v = dyad
        if u not in nodes_in_matching and v not in nodes_in_matching:
            matching.add((u,v))
            nodes_in_matching.update({u,v})

    if len(matching) == ideal_matching_size:
        interaction_sequence.append(matching)
        print("Matching added to sequence")
        for matched in matching:
            dyads.remove(matched)
        print(f"{len(dyads)} remain for matching")
        if len(interaction_sequence) == rounds:
            break
    
    if tries_since_ideal_matching > 1000:
        ideal_matching_size -= 1
        print(f"new ideal matching size: {ideal_matching_size}")
        tries_since_ideal_matching = 0
    
    tries -= 1
    tries_since_ideal_matching += 1

print(f"Interaction sequence for {rounds} rounds found:")
interaction_sequence

The completion of this issue requires:

• Refactor from playground.ipynb to a new src/sequence.py method
• Take interactions parameters after validate_config(study_name) as input for sequence
• Enforce a range of interactions that must exist per participant for a given number of rounds
• Return a JavaScript aware data structure of the sequence