The difference between PN and CC is only at the training stage.

Combinatorial Optimization (CO) problems over graphs appear routinely in many applications such as in optimizing traffic, viral marketing in social networks, and matching for job allocation. Due to their combinatorial nature, these problems are often NP-hard. Existing approximation algorithms and heuristics rely on the search space to find the solutions and become time-consuming when this space is large. In this paper, we design a neural method called COMBHelper to reduce this space and thus improve the efficiency of the traditional CO algorithms based on node selection. Specifically, it employs a Graph Neural Network (GNN) to identify promising nodes for the solution set. This pruned search space is then fed to the traditional CO algorithms. COMBHelper also uses a Knowledge Distillation (KD) module and a problem-specific boosting module to bring further efficiency and efficacy. Our extensive experiments show that the traditional CO algorithms with COMBHelper are at least 2 times faster than their original versions.

This paper surveys the recent attempts, both from the machine learning and operations research communities, at leveraging machine learning to solve combinatorial optimization problems. Given the hard nature of these problems, state-of-the-art methodologies involve algorithmic decisions that either require too much computing time or are not mathematically well defined. Thus, machine learning looks like a promising candidate to effectively deal with those decisions. We advocate for pushing further the integration of machine learning and combinatorial optimization and detail methodology to do so. A main point of the paper is seeing generic optimization problems as data points and inquiring what is the relevant distribution of problems to use for learning on a given task.

The problem of organizing information for multidocument summarization so that the generated summary is coherent has received relatively little attention. While sentence ordering for single document summarization can be determined from the ordering of sentences in the input article, this is not the case for multidocument summarization where summary sentences may be drawn from different input articles. In this paper, we propose a methodology for studying the properties of ordering information in the news genre and describe experiments done on a corpus of multiple acceptable orderings we developed for the task. Based on these experiments, we implemented a strategy for ordering information that combines constraints from chronological order of events and topical relatedness. Evaluation of our augmented algorithm shows a significant improvement of the ordering over two baseline strategies.

The problem of organizing information for multidocument summarization so that the generated summary is coherent has received relatively little attention. While sentence ordering for single document summarization can be determined from the ordering of sentences in the input article, this is not the case for multidocument summarization where summary sentences may be drawn from different input articles. In this paper, we propose a methodology for studying the properties of ordering information in the news genre and describe experiments done on a corpus of multiple acceptable orderings we developed for the task. Based on these experiments, we implemented a strategy for ordering information that combines constraints from chronological order of events and topical relatedness. Evaluation of our augmented algorithm shows a significant improvement of the ordering over two baseline strategies.