# Mittagsseminar (in cooperation with A. Steger, D. Steurer and B. Sudakov)

__Mittagsseminar Talk Information__ | |

**Date and Time**: Thursday, December 14, 2023, 12:15 pm

**Duration**: 30 minutes

**Location**: CAB G51

**Speaker**: Ulysse Schaller

## Balanced Bidirectional Breadth-First-Search on Scale-Free Networks

To find a shortest path between two nodes s and t in a given graph, a classical approach is to start a Breadth-First Search (BFS) from s and run it until the search discovers t. Alternatively, one can start two Breadth First Searches, one from s and one from t, and alternate their layer expansions until they meet. This bidirectional BFS can be balanced by always expanding a layer on the side that has seen fewer vertices so far. This usually results in significant speedups in real-world networks, and it has been shown that this indeed yields sublinear running time on scale-free graph models such as Chung-Lu graphs and GIRGs. We improve this layer-balanced bidirectional BFS approach by using a finer balancing technique. Instead of comparing the size of the two BFS trees after each layer expansion, we perform this comparison after each vertex expansion. This gives rise to two algorithms that run faster than the layer-balanced bidirectional BFS on scale-free networks with power-law exponent 2 < tau < 3. The first one is an approximate shortest-path algorithm that outputs a path of length at most 1 longer than the shortest path in time n^{(tau-2)/(tau-1)+o(1)}. The second one is an exact shortest-path algorithm running in time n^{1/2+o(1)}. These runtime bounds hold with high probability when s and t are chosen uniformly at random among the n vertices of the graph. We also develop an edge-balanced bidirectional BFS algorithm that works under adversarial conditions. This approximate shortest-path algorithm runs in time n^{1/2+o(1)} with high probability when the adversary is allowed to choose s and t based on their (expected) degree. This is joint work with Sacha Cerf, Benjamin Dayan, Umberto De Ambroggio, Marc Kaufmann, and Johannes Lengler.

Upcoming talks | All previous talks | Talks by speaker | Upcoming talks in iCal format (beta version!)

Previous talks by year: 2024 2023 2022 2021 2020 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996

Information for students and suggested topics for student talks

Automatic MiSe System Software Version 1.4803M | admin login