Ben Strasser

Intriguingly Simple and Fast Transit Routing

This paper studies the problem of computing optimal journeys in dynamic public transit networks. We introduce a novel algorithmic framework, called Connection Scan Algorithm (CSA), to compute journeys. It organizes data as a single array of connections, which it scans once per query. Despite its simplicity, our algorithm is very versatile. We use it to solve earliest arrival and multi-criteria profile queries. Moreover, we extend it to handle the minimum expected arrival time (MEAT) problem, which incorporates stochastic delays on the vehicles and asks for a set of (alternative) journeys that in its entirety minimizes the user’s expected arrival time at the destination. Our experiments on the dense metropolitan network of London show that CSA computes MEAT queries, our most complex scenario, in 272 ms on average.

Customizable Contraction Hierarchies

We consider the problem of quickly computing shortest paths in weighted graphs given auxiliary data derived in an expensive preprocessing phase. By adding a fast weight-customization phase, we extend Contraction Hierarchies [12] to support the three-phase workflow introduced by Delling et al. [6]. Our Customizable Contraction Hierarchies use nested dissection orders as suggested in [3]. We provide an in-depth experimental analysis on large road and game maps that clearly shows that Customizable Contraction Hierarchies are a very practicable solution in scenarios where edge weights often change.

Graph Bisection with Pareto Optimization

We introduce FlowCutter, a novel algorithm to compute a set of edge cuts or node separators that optimize cut size and balance in the Pareto sense. Our core algorithm heuristically solves the balanced connected st-edge-cut problem, where two given nodes s and t must be separated by removing edges to obtain two connected parts. Using the core algorithm as a subroutine, we build variants that compute node separators that are independent of s and t. From the computed Pareto set, we can identify cuts with a particularly good tradeoff between cut size and balance that can be used to compute contraction and minimum fill-in orders, which can be used in Customizable Contraction Hierarchies (CCHs), a speed-up technique for shortest-path computations. Our core algorithm runs in O(c∣E∣) time, where E is the set of edges and c is the size of the largest outputted cut. This makes it well suited for separating large graphs with small cuts, such as road graphs, which is the primary application motivating our research. For road graphs, we present an extensive experimental study demonstrating that FlowCutter outperforms the current state of the art in terms of both cut sizes and CCH performance. By evaluating FlowCutter on a standard graph partitioning benchmark, we further show that FlowCutter also finds small, balanced cuts on nonroad graphs. Another application is the computation of small tree decompositions. To evaluate the quality of our algorithm in this context, we entered the PACE 2016 challenge [13] and won first place in the corresponding sequential competition track. We can therefore conclude that our FlowCutter algorithm finds small, balanced cuts on a wide variety of graphs.

Fast exact shortest path and distance queries on road networks with parametrized costs

We study a scenario for route planning in road networks, where the objective to be optimized may change between every shortest path query. Since this invalidates many of the known speedup techniques for road networks that are based on preprocessing of shortest path structures, we investigate optimizations exploiting topological structures. We experimentally evaluate our technique on a large set of real-world road networks of various data sources. With lightweight preprocessing our technique answers long-distance queries across continental networks significantly faster than previous approaches towards the same problem formulation.

Delay-Robust Journeys in Timetable Networks with Minimum Expected Arrival Time

We study the problem of computing delay-robust routes in timetable networks. Instead of a single path we compute a decision graph containing all stops and trains/vehicles that might be relevant. Delays are formalized using a stochastic model. We show how to compute a decision graph that minimizes the expected arrival time while bounding the latest arrival time over all sub-paths. Finally we show how the information contained within a decision graph can compactly be represented to the user. We experimentally evaluate our algorithms and show that the running times allow for interactive usage on a realistic train network. 1998 ACM Subject Classification G.2.2 Graph Theory

Fast Quasi-Threshold Editing

We introduce Quasi-Threshold Mover (QTM), an algorithm to solve the quasi-threshold (also called trivially perfect) graph editing problem with a minimum number of edge insertions and deletions. Given a graph it computes a quasi-threshold graph which is close in terms of edit count, but not necessarily closest as this edit problem is NP-hard. We present an extensive experimental study, in which we show that QTM performs well in practice and is the first heuristic that is able to scale to large real-world graphs in practice. As a side result we further present a simple linear-time algorithm for the quasi-threshold recognition problem.

Compressing optimal paths with run length encoding

We introduce a novel approach to Compressed Path Databases, space efficient oracles used to very quickly identify the first edge on a shortest path. Our algorithm achieves query running times on the 100 nanosecond scale, being significantly faster than state-of-the-art first-move oracles from the literature. Space consumption is competitive, due to a compression approach that rearranges rows and columns in a first-move matrix and then performs run length encoding (RLE) on the contents of the matrix. One variant of our implemented system was, by a convincing margin, the fastest entry in the 2014 Grid-Based Path Planning Competition. We give a first tractability analysis for the compression scheme used by our algorithm. We study the complexity of computing a database of minimum size for general directed and undirected graphs. We find that in both cases the problem is NP-complete. We also show that, for graphs which can be decomposed along articulation points, the problem can be decomposed into independent parts, with a corresponding reduction in its level of difficulty. In particular, this leads to simple and tractable algorithms with linear running time which yield optimal compression results for trees.

Efficient Traffic Assignment for Public Transit Networks

We study the problem of computing traffic assignments for public transit networks: Given a public transit network and a demand (i.e. a list of passengers, each with associated origin, destination, and departure time), the objective is to compute the utilization of every vehicle. Efficient assignment algorithms are a core component of many urban traffic planning tools. In this work, we present a novel algorithm for computing public transit assignments. Our approach is based upon a microscopic Monte Carlo simulation of individual passengers. In order to model realistic passenger behavior, we base all routing decisions on travel time, number of transfers, time spent walking or waiting, and delay robustness. We show how several passengers can be processed during a single scan of the network, based on the Connection Scan Algorithm [Dibbelt et al., LNCS Springer 2013], resulting in a highly efficient algorithm. We conclude with an experimental study, showing that our assignments are comparable in terms of quality to the state-of-the-art. Using the parallelized version of our algorithm, we are able to compute a traffic assignment for more than ten million passengers in well below a minute, which outperforms previous works by more than an order of magnitude.

Erratum: Customizable Contraction Hierarchies

All customization running times in this article are reported to be in milliseconds. This is unfortunately a mistake. The correct unit is seconds. This is especially the case for the reported CRP customization times. All comparisons between our method and CRP are therefore still valid as the compared numbers are wrong by the same factor.

Distributed Graph Clustering Using Modularity and Map Equation

We study large-scale, distributed graph clustering. Given an undirected, weighted graph, our objective is to partition the nodes into disjoint sets called clusters. Each cluster should contain many internal edges. Further, there should only be few edges between clusters. We study two established formalizations of this internally-dense-externally-sparse principle: modularity and map equation. We present two versions of a simple distributed algorithm to optimize both measures. They are based on Thrill, a distributed big data processing framework that implements an extended MapReduce model. The algorithms for the two measures, DSLM-Mod and DSLM-Map, differ only slightly. Adapting them for similar quality measures is easy. In an extensive experimental study, we demonstrate the excellent performance of our algorithms on real-world and synthetic graph clustering benchmark graphs.