Faster Global Minimum Cut with Predictions

Helia Niaparast, Benjamin Moseley, Karan Singh

TL;DR: We incorporate predictions into Karger and Karger-Stein algorithms to develop faster methods for finding the global minimum cut.

Abstract:

Global minimum cut is a fundamental combinatorial optimization problem with wide-ranging applications. Often in practice, these problems are solved repeatedly on families of similar or related instances. However, the de facto algorithmic approach is to solve each instance of the problem from scratch discarding information from prior instances.

In this paper, we consider how predictions informed by prior instances can be used to warm-start practical minimum cut algorithms. The paper considers the widely used Karger's algorithm and its counterpart, the Karger-Stein algorithm. Given good predictions, we show these algorithms become near-linear time and have robust performance to erroneous predictions. Both of these algorithms are randomized edge-contraction algorithms. Our natural idea is to probabilistically prioritize the contraction of edges that are unlikely to be in the minimum cut.

Lay Summary:

Solving Network Problems Faster by Learning from the Past

Many real-world problems involve breaking a network, like a transportation map or a social network, into two parts while cutting as few connections as possible. This kind of task arises in areas like data analysis, communication systems, and machine learning.

Often, similar versions of the problem are solved over and over. But most methods start from scratch each time, without using what was learned from earlier problems.

In this work, we explore how to speed things up by using predictions based on past experience. We focus on two well-known methods that solve the problem by repeatedly merging parts of the network at random until only two groups remain. Normally, this merging process is completely random, which helps the algorithms to find the best solution most of the time after a sufficient number of attempts, but it can also be slow.

We show that by guiding the process using predictions and favoring merges that are likely to be safe based on earlier problems, we can solve new ones much faster. Even when the predictions are not perfect, the performance stays strong.

This makes it more practical to handle repeated or related network problems quickly, which is common in real-world applications.

Link To Code: https://github.com/helia-niaparast/global-minimum-cut-with-predictions

Primary Area: Optimization->Discrete and Combinatorial Optimization

Keywords: Algorithms with Predictions, Minimum Cut, Karger, Karger-Stein

Submission Number: 14171