Satisfiability by Maxwell-Boltzmann and Bose-Einstein Statistical Distributions

Recent studies in theoretical computer science have exploited new algorithms and methodologies based on statistical physics for investigating the structure and the properties of the Satisfiability (SAT) problem. We propose a characterization of the SAT problem as a physical system, using both quantum and classi-cal statistical-physical models. We associate a graph to an SAT instance and we prove that a Bose-Einstein condensation occurs in the instance with higher probability if the quantum distribution is adopted in the gen-eration of the graph. Conversely, the fit-get-rich behavior is more likely if we adopt the Maxwell-Boltzmann distribution. Our method allows a comprehensive analysis of the SAT problem based on a new definition of entropy of an instance, without requiring the computation of its truth assignments. The entropy of an SAT instance increases in the satisfiability region as the number of free variables in the instance increases. Finally, we develop six new solvers for the MaxSAT problem based on quantum and classical statistical dis-tributions, and we test them on random SAT instances, with competitive results. We experimentally prove that the performance of the solvers based on the two distributions depends on the criterion used to flag clauses as satisfied in the SAT solving process

Trip-Based Public Transit Routing Using Condensed Search Trees

We study the problem of planning Pareto-optimal journeys in public transit networks. Most existing algorithms and speed-up techniques work by computing subjourneys to intermediary stops until the destination is reached. In contrast, the trip-based model focuses on trips and transfers between them, constructing journeys as a sequence of trips. In this paper, we develop a speed-up technique for this model inspired by principles behind existing state-of-the-art speed-up techniques, Transfer Pattern and Hub Labelling. The resulting algorithm allows us to compute Pareto-optimal (with respect to arrival time and number of transfers) 24-hour profiles on very large real-world networks in less than half a millisecond. Compared to the current state of the art for bicriteria queries on public transit networks, this is up to two orders of magnitude faster, while increasing preprocessing overhead by at most one order of magnitude

PACE Solver Description: Tree Depth with FlowCutter

We describe the FlowCutter submission to the PACE 2020 heuristic tree-depth challenge. The task of the challenge consists of computing an elimination tree of small height for a given graph. At its core our submission uses a nested dissection approach, with FlowCutter as graph bisection algorithm

On the External Validity of Average-Case Analyses of Graph Algorithms

The number one criticism of average-case analysis is that we do not actually know the probability distribution of real-world inputs. Thus, analyzing an algorithm on some random model has no implications for practical performance. At its core, this criticism doubts the existence of external validity, i.e., it assumes that algorithmic behavior on the somewhat simple and clean models does not translate beyond the models to practical performance real-world input. With this paper, we provide a first step towards studying the question of external validity systematically. To this end, we evaluate the performance of six graph algorithms on a collection of 2751 sparse real-world networks depending on two properties; the heterogeneity (variance in the degree distribution) and locality (tendency of edges to connect vertices that are already close). We compare this with the performance on generated networks with varying locality and heterogeneity. We find that the performance in the idealized setting of network models translates surprisingly well to real-world networks. Moreover, heterogeneity and locality appear to be the core properties impacting the performance of many graph algorithms

On the External Validity of Average-Case Analyses of Graph Algorithms

The number one criticism of average-case analysis is that we do not actually know the probability distribution of real-world inputs. Thus, analyzing an algorithm on some random model has no implications for practical performance. At its core, this criticism doubts the existence of external validity, i.e., it assumes that algorithmic behavior on the somewhat simple and clean models does not translate beyond the models to practical performance real-world input. With this paper, we provide a first step towards studying the question of external validity systematically. To this end, we evaluate the performance of six graph algorithms on a collection of 2751 sparse real-world networks depending on two properties; the heterogeneity (variance in the degree distribution) and locality (tendency of edges to connect vertices that are already close). We compare this with the performance on generated networks with varying locality and heterogeneity. We find that the performance in the idealized setting of network models translates surprisingly well to real-world networks. Moreover, heterogeneity and locality appear to be the core properties impacting the performance of many graph algorithms