9 papers
An Evaluation of Vertex Elimination Strategies for Algorithmic Differentiation
Alex Crane, Pål Grønås Drange, Eli Friedman +6
The algorithmic differentiation (AD) of mathematical functions can be interpreted as a sequence of vertex eliminations in an underlying directed acyclic graph. The problem of deter…
Structural Optimal Jacobian Accumulation and Minimum Edge Count are NP-Complete Under Vertex Elimination
Matthias Bentert, Alex Crane, Pål Grønås Drange +2
We study graph-theoretic formulations of two fundamental problems in algorithmic differentiation. The first (Structural Optimal Jacobian Accumulation) is that of computing a Jacobi…
Preprocessing to Reduce the Search Space for Odd Cycle Transversal
Bart M. P. Jansen, Yosuke Mizutani, Blair D. Sullivan +1
The NP-hard Odd Cycle Transversal problem asks for a minimum vertex set whose removal from an undirected input graph breaks all odd cycles, and thereby yields a bipartite graph…
A Space-Efficient Algebraic Approach to Robotic Motion Planning
Matthias Bentert, Daniel Coimbra Salomao, Alex Crane +3
We consider efficient route planning for robots in applications such as infrastructure inspection and automated surgical imaging. These tasks can be modeled via the combinatorial p…
Leveraging Fixed-Parameter Tractability for Robot Inspection Planning
Yosuke Mizutani, Daniel Coimbra Salomao, Alex Crane +5
Autonomous robotic inspection, where a robot moves through its environment and inspects points of interest, has applications in industrial settings, structural health monitoring, a…
Open Problems in (Hyper)Graph Decomposition
Deepak Ajwani, Rob H. Bisseling, Katrin Casel +26
Large networks are useful in a wide range of applications. Sometimes problem instances are composed of billions of entities. Decomposing and analyzing these structures helps us gai…
Improved Parameterized Complexity of Happy Set Problems
Yosuke Mizutani, Blair D. Sullivan
We present fixed-parameter tractable (FPT) algorithms for two problems, Maximum Happy Set (MaxHS) and Maximum Edge Happy Set (MaxEHS)--also known as Densest k-Subgraph. Given a gra…
Faster Decomposition of Weighted Graphs into Cliques using Fisher's Inequality
Shweta Jain, Yosuke Mizutani, Blair Sullivan
Mining groups of genes that consistently co-express is an important problem in biomedical research, where it is critical for applications such as drug-repositioning and designing n…
Minimizing Congestion for Balanced Dominators
Yosuke Mizutani, Annie Staker, Blair D. Sullivan
A primary challenge in metagenomics is reconstructing individual microbial genomes from the mixture of short fragments created by sequencing. Recent work leverages the sparsity of…