Minimum sum coloring for large graphs with extraction and backward expansion search

The Minimum Sum Coloring Problem (MSCP) is a relevant model tightly related to the classical vertex coloring problem (VCP). MSCP is known to be NP-hard, thus solving the problem for large graphs is particular challenging. Based on the general “reduce-and-solve” principle and inspired by the work for the VCP, we present an extraction and backward expansion search approach (EBES) to compute the upper and lower bounds for the MSCP on large graphs. The extraction phase reduces the given graph by extracting large collections of pairwise disjoint large independent sets (or color classes). The backward extension phase adds the extracted independent sets to recover the intermediate graphs while optimizing the sum coloring of each intermediate graph. We assess the proposed approach on a set of 35 large benchmark graphs with 450–4000 vertices from the DIMACS and COLOR graph coloring competitions. Computational results show that EBES is able to find improved upper bounds for 19 graphs and improved lower bounds for 12 graphs

Air traffic deconfliction using sum coloring

Best of Session (UTM-6: sUAS Traffic Management and Deconfliction) Award, 38 DASC 38th IEEE/AIAA Digital Avionics Systems ConferenceThis paper studies strategic conflict resolution for air traffic based on sum coloring. We consider two application scenarios: manned and unmanned air traffic, with similar targets: to improve efficiency of operations and to reduce the costs. For the Unmanned Air Vehicles Traffic Management (UTM) we consider also a payment mechanism which incentivizes the operators to share information necessary to find a socially optimal solution. We quantify the potential savings via a series of experiments, showing that our methods drastically outperform the widely used First-Come-First-Serve (FCFS) strategy.Peer ReviewedAward-winningPostprint (published version

Lower Bound for (Sum) Coloring Problem

The Minimum Sum Coloring Problem is a variant of the Graph Vertex Coloring Problem, for which each color has a weight. This paper presents a new way to find a lower bound of this problem, based on a relaxation into an integer partition problem with additional constraints. We improve the lower bound for 18 graphs of standard benchmark DIMACS, and prove the optimal value for 4 graphs by reaching their known upper bound

LIPIcs, Volume 244, ESA 2022, Complete Volume

LIPIcs, Volume 244, ESA 2022, Complete Volum

Classical Planning in Deep Latent Space

Current domain-independent, classical planners require symbolic models of the problem domain and instance as input, resulting in a knowledge acquisition bottleneck. Meanwhile, although deep learning has achieved significant success in many fields, the knowledge is encoded in a subsymbolic representation which is incompatible with symbolic systems such as planners. We propose Latplan, an unsupervised architecture combining deep learning and classical planning. Given only an unlabeled set of image pairs showing a subset of transitions allowed in the environment (training inputs), Latplan learns a complete propositional PDDL action model of the environment. Later, when a pair of images representing the initial and the goal states (planning inputs) is given, Latplan finds a plan to the goal state in a symbolic latent space and returns a visualized plan execution. We evaluate Latplan using image-based versions of 6 planning domains: 8-puzzle, 15-Puzzle, Blocksworld, Sokoban and Two variations of LightsOut.Comment: Under review at Journal of Artificial Intelligence Research (JAIR