Léon R. Planken

Computing all-pairs shortest paths by leveraging low treewidth

Considering directed graphs on n vertices and m edges with real (possibly negative) weights, we present two new, efficient algorithms for computing all-pairs shortest paths (APSP). These algorithms make use of directed path consistency (DPC) along a vertex ordering d. The algorithms run in O(n2wd) time, where wd is the graph width induced by this vertex ordering. For graphs of constant treewidth, this yields O(n2) time, which is optimal. On chordal graphs, the algorithms run in O(nm) time. We show empirically that also in many general cases, both constructed and from realistic benchmarks, the algorithms often outperform Johnsons algorithm, which represents the current state of the art with a run time of O (nm + n2 log n). These algorithms can be used for temporal and spatial reasoning, e.g. for the Simple Temporal Problem (STP), which underlines its relevance to the planning and scheduling community.

Mechanism Design for the Online Allocation of Items without Monetary Payments

We consider online mechanism design without money, where agents are allowed to trade items with other agents, in an attempt to improve their own allocation. In an off-line context, this problem is known as the House Allocation Problem (HAP). We extend HAP to an online problem and call it the Online House Allocation Problem (OHAP). In OHAP, agents can choose when to arrive and depart over time and are allowed to be indifferent between items. Subsequently, we present our Agent Shifting Algorithm (ASA) for OHAP. A mechanism that uses ASA as its allocation rule is shown to be strategy-proof, individually rational and Pareto optimal. Moreover, we argue that any mechanism that obtains an outcome in OHAP that cannot be obtained by using ASA fails to be strategy-proof or is not Pareto optimal.