A Partitioning Algorithm for Maximum Common Subgraph Problems

We introduce a new branch and bound algorithm for the maximum common subgraph and maximum common connected subgraph problems which is based around vertex labelling and partitioning. Our method in some ways resembles a traditional constraint programming approach, but uses a novel compact domain store and supporting inference algorithms which dramatically reduce the memory and computation requirements during search, and allow better dual viewpoint ordering heuristics to be calculated cheaply. Experiments show a speedup of more than an order of magnitude over the state of the art, and demonstrate that we can operate on much larger graphs without running out of memory

"Almost-stable" matchings in the Hospitals / Residents problem with Couples

The Hospitals / Residents problem with Couples (hrc) models the allocation of intending junior doctors to hospitals where couples are allowed to submit joint preference lists over pairs of (typically geographically close) hospitals. It is known that a stable matching need not exist, so we consider min bp hrc, the problem of finding a matching that admits the minimum number of blocking pairs (i.e., is “as stable as possible”). We show that this problem is NP-hard and difficult to approximate even in the highly restricted case that each couple finds only one hospital pair acceptable. However if we further assume that the preference list of each single resident and hospital is of length at most 2, we give a polynomial-time algorithm for this case. We then present the first Integer Programming (IP) and Constraint Programming (CP) models for min bp hrc. Finally, we discuss an empirical evaluation of these models applied to randomly-generated instances of min bp hrc. We find that on average, the CP model is about 1.15 times faster than the IP model, and when presolving is applied to the CP model, it is on average 8.14 times faster. We further observe that the number of blocking pairs admitted by a solution is very small, i.e., usually at most 1, and never more than 2, for the (28,000) instances considered

PACE Solver Description: Bute-Plus: A Bottom-Up Exact Solver for Treedepth

This note introduces Bute-Plus, an exact solver for the treedepth problem. The core of the solver is a positive-instance driven dynamic program that constructs an elimination tree of minimum depth in a bottom-up fashion. Three features greatly improve the algorithm's run time. The first of these is a specialised trie data structure. The second is a domination rule. The third is a heuristic presolve step can quickly find a treedepth decomposition of optimal depth for many instances.Comment: 4 pages, 1 appendix pages, 0 figures. A version of this tool description paper without the appendix is published in the proceedings of IPEC 2020: https://drops.dagstuhl.de/opus/volltexte/2020/13337/pdf/LIPIcs-IPEC-2020-34.pdf . Changes: this version expands the paper from a preliminary versio

Network connectivity tracking for a team of unmanned aerial vehicles

Algebraic connectivity is the second-smallest eigenvalue of the Laplacian matrix and can be used as a metric for the robustness and efficiency of a network. This connectivity concept applies to teams of multiple unmanned aerial vehicles (UAVs) performing cooperative tasks, such as arriving at a consensus. As a UAV team completes its mission, it often needs to control the network connectivity. The algebraic connectivity can be controlled by altering edge weights through movement of individual UAVs in the team, or by adding and deleting edges. The addition and deletion problem for algebraic connectivity, however, is NP-hard. The contributions of this work are 1) a comparison of four heuristic methods for modifying algebraic connectivity through the addition and deletion of edges, 2) a rule-based algorithm for tracking a connectivity profile through edge weight modification and the addition and deletion of edges, 3) a new, hybrid method for selecting the best edge to add or remove, 4) a distributed method for estimating the eigenvectors of the Laplacian matrix and selecting the best edge to add or remove for connectivity modification and tracking, and 5) an implementation of the distributed connectivity tracking using a consensus controller and double-integrator dynamics

An Algorithm for the Exact Treedepth Problem

We present a novel algorithm for the minimum-depth elimination tree problem, which is equivalent to the optimal treedepth decomposition problem. Our algorithm makes use of two cheaply-computed lower bound functions to prune the search tree, along with symmetry-breaking and domination rules. We present an empirical study showing that the algorithm outperforms the current state-of-the-art solver (which is based on a SAT encoding) by orders of magnitude on a range of graph classes

PACE Solver Description: Tweed-Plus: A Subtree-Improving Heuristic Solver for Treedepth

This paper introduces Tweed-Plus, a heuristic solver for the treedepth problem. The solver uses two well-known algorithms to create an initial elimination tree: nested dissection (making use of the Metis library) and the minimum-degree heuristic. After creating an elimination tree of the entire input graph, the solver continues to apply nested dissection and the minimum-degree heuristic to parts of the graph with the aim of replacing subtrees of the elimination tree with alternatives of lower depth

International Law of Outer Space and its Effect on Commercial Space Activity

The United Nations, through a series of five treaties, has created a body of international space law which controls the activities in space of states, international organizations, and private interests. Corporations planning an investment in commercial space ventures must consider the restrictions and obligations which space law will impose on their activities. This article discusses the substantive principles of the law of outer space and focuses on those provisions which will affect commercial space activities