3 research outputs found
Finding Near-Optimal Weight Independent Sets at Scale
Computing maximum weight independent sets in graphs is an important NP-hard
optimization problem. The problem is particularly difficult to solve in large
graphs for which data reduction techniques do not work well. To be more
precise, state-of-the-art branch-and-reduce algorithms can solve many
large-scale graphs if reductions are applicable. Otherwise, their performance
quickly degrades due to branching requiring exponential time. In this paper, we
develop an advanced memetic algorithm to tackle the problem, which incorporates
recent data reduction techniques to compute near-optimal weighted independent
sets in huge sparse networks. More precisely, we use a memetic approach to
recursively choose vertices that are likely to be in a large-weight independent
set. We include these vertices into the solution, and further reduce the graph.
We show that identifying and removing vertices likely to be in large-weight
independent sets opens up the reduction space and speeds up the computation of
large-weight independent sets remarkably. Our experimental evaluation indicates
that we are able to outperform state-of-the-art algorithms. For example, our
two algorithm configurations compute the best results among all competing
algorithms for 205 out of 207 instances. Thus can be seen as a useful tool when
large-weight independent sets need to be computed in~practice
Finding Optimal 2-Packing Sets on Arbitrary Graphs at Scale
A 2-packing set for an undirected graph is a subset such that any two vertices have no common
neighbors. Finding a 2-packing set of maximum cardinality is a NP-hard problem.
We develop a new approach to solve this problem on arbitrary graphs using its
close relation to the independent set problem. Thereby, our algorithm red2pack
uses new data reduction rules specific to the 2-packing set problem as well as
a graph transformation. Our experiments show that we outperform the
state-of-the-art for arbitrary graphs with respect to solution quality and also
are able to compute solutions multiple orders of magnitude faster than
previously possible. For example, we are able to solve 63% of our graphs to
optimality in less than a second while the competitor for arbitrary graphs can
only solve 5% of the graphs in the data set to optimality even with a 10 hour
time limit. Moreover, our approach can solve a wide range of large instances
that have previously been unsolved
Arc-Flags Meet Trip-Based Public Transit Routing
We present Arc-Flag TB, a journey planning algorithm for public transit
networks which combines Trip-Based Public Transit Routing (TB) with the
Arc-Flags speedup technique. Compared to previous attempts to apply Arc-Flags
to public transit networks, which saw limited success, our approach uses
stronger pruning rules to reduce the search space. Our experiments show that
Arc-Flag TB achieves a speedup of up to two orders of magnitude over TB,
offering query times of less than a millisecond even on large countrywide
networks. Compared to the state-of-the-art speedup technique Trip-Based Public
Transit Routing Using Condensed Search Trees (TB-CST), our algorithm achieves
similar query times but requires significantly less additional memory. Other
state-of-the-art algorithms which achieve even faster query times, e.g., Public
Transit Labeling, require enormous memory usage. In contrast, Arc-Flag TB
offers a tradeoff between query performance and memory usage due to the fact
that the number of regions in the network partition required by our algorithm
is a configurable parameter. We also identify an issue in the transfer
precomputation of TB that affects both TB-CST and Arc-Flag TB, leading to
incorrect answers for some queries. This has not been previously recognized by
the author of TB-CST. We provide discussion on how to resolve this issue in the
future. Currently, Arc-Flag TB answers 1-6% of queries incorrectly, compared to
over 20% for TB-CST on some networks