Finding Near-Optimal Independent Sets at Scale

The independent set problem is NP-hard and particularly difficult to solve in large sparse graphs. In this work, we develop an advanced evolutionary algorithm, which incorporates kernelization techniques to compute large independent sets in huge sparse networks. A recent exact algorithm has shown that large networks can be solved exactly by employing a branch-and-reduce technique that recursively kernelizes the graph and performs branching. However, one major drawback of their algorithm is that, for huge graphs, branching still can take exponential time. To avoid this problem, we recursively choose vertices that are likely to be in a large independent set (using an evolutionary approach), then further kernelize the graph. We show that identifying and removing vertices likely to be in large independent sets opens up the reduction space---which not only speeds up the computation of large independent sets drastically, but also enables us to compute high-quality independent sets on much larger instances than previously reported in the literature.Comment: 17 pages, 1 figure, 8 tables. arXiv admin note: text overlap with arXiv:1502.0168

Faster Batched Shortest Paths in Road Networks

We study the problem of computing batched shortest paths in road networks efficiently. Our focus is on computing paths from a single source to multiple targets (one-to-many queries). We perform a comprehensive experimental comparison of several approaches, including new ones. We conclude that a new extension of PHAST (a recent one-to-all algorithm), called RPHAST, has the best performance in most cases, often by orders of magnitude. When used to compute distance tables (many-to-many queries), RPHAST often outperforms all previous approaches

Route Planning in Transportation Networks

We survey recent advances in algorithms for route planning in transportation networks. For road networks, we show that one can compute driving directions in milliseconds or less even at continental scale. A variety of techniques provide different trade-offs between preprocessing effort, space requirements, and query time. Some algorithms can answer queries in a fraction of a microsecond, while others can deal efficiently with real-time traffic. Journey planning on public transportation systems, although conceptually similar, is a significantly harder problem due to its inherent time-dependent and multicriteria nature. Although exact algorithms are fast enough for interactive queries on metropolitan transit systems, dealing with continent-sized instances requires simplifications or heavy preprocessing. The multimodal route planning problem, which seeks journeys combining schedule-based transportation (buses, trains) with unrestricted modes (walking, driving), is even harder, relying on approximate solutions even for metropolitan inputs.Comment: This is an updated version of the technical report MSR-TR-2014-4, previously published by Microsoft Research. This work was mostly done while the authors Daniel Delling, Andrew Goldberg, and Renato F. Werneck were at Microsoft Research Silicon Valle

Robust Mobile Route Planning with Limited Connectivity

We study the problem of route planning on mobile devices. There are two current approaches to this problem. One option is to have all the routing data on the device, which can then compute routes by itself. This makes it hard to incorporate traffic updates, leading to suboptimal routes. An alternative approach outsources the route computation to a server, which then sends only the route to the device. The downside is that a user is lost when deviating from the proposed route in an area with limited connectivity. In this work, we present an approach that combines the best of both worlds. The server performs the route computation but, instead of sending only the route to the user, it sends a corridor that is robust against deviations. We define these corridors properly and show that their size can be theoretically bounded in road networks. We evaluate their quality experimentally in terms of size and robustness on a continental road network. Finally, we introduce several algorithms to compute corridors efficiently. Our experimental analysis shows that our corridors are small but very robust against deviations, and can be computed quickly on a standard server

ANALYSIS OF DISCRIMINATORY GAME VARIABLES BETWEEN WINNERS AND LOSERS IN WOMEN’S HANDBALL WORLD CHAMPIONSHIPS FROM 2007 TO 2017

The aim of this study was to identify game variables that discriminated winning from losing teams and to understand how these variables contributed to victory by observing goal differences in matches of the women’s handball world championships. The sample comprised 471 WCh’s games played between 2007 and 2017. The games were grouped into three clusters: balanced games – difference of 1-8 goals; unbalanced games – difference of 9-20 goals; and very unbalanced games – difference of > 20 goals. Generally, the performance of winning teams was significantly higher (in most variables), or lower in the case of the number of technical faults (p<.05). In the balanced games, there was a greater contribution of defensive variables (stolen balls, blocked throws, and goalkeeper’s efficiency indicators) in relation to attack variables (attack efficiency and throw efficiency indicators). For victory, the number of technical faults reduce the chances of winning. Games with the unbalanced and very unbalanced goal differences seem to follow the same tendency; however, in the very unbalanced games, there were more assists, yellow cards and 2-min suspensions. We concluded that the decisive variables for victory in the balanced games showed a greater weight, with a special emphasis on stolen balls followed by offensive variables (throw efficiency indicators, attack efficiency, and technical faults). There was an equal tendency for the games with unbalanced and very unbalanced outcomes