Delaying Decisions and Reservation Costs
Elisabet Burjons, Fabian Frei, Matthias Gehnen, Henri Lotze, Daniel, Mock, Peter Rossmanith

TL;DR
This paper investigates online algorithms for Feedback Vertex Set and Vertex Cover problems with delayed decisions and reservation options, establishing bounds on their competitive ratios and analyzing how reservations impact online decision-making.
Contribution
It introduces a novel online model with delayed decisions and reservations, providing bounds on competitive ratios for these problems under the new model.
Findings
Feedback Vertex Set has a competitive ratio between 4 and 5 with delayed decisions.
Reservations can improve competitive ratios, bounded by functions of reservation cost.
Vertex Cover with reservations achieves a competitive ratio of min{1+2α, 2}.
Abstract
We study the Feedback Vertex Set and the Vertex Cover problem in a natural variant of the classical online model that allows for delayed decisions and reservations. Both problems can be characterized by an obstruction set of subgraphs that the online graph needs to avoid. In the case of the Vertex Cover problem, the obstruction set consists of an edge (i.e., the graph of two adjacent vertices), while for the Feedback Vertex Set problem, the obstruction set contains all cycles. In the delayed-decision model, an algorithm needs to maintain a valid partial solution after every request, thus allowing it to postpone decisions until the current partial solution is no longer valid for the current request. The reservation model grants an online algorithm the new and additional option to pay a so-called reservation cost for any given element in order to delay the decision of adding or…
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Taxonomy
TopicsOptimization and Search Problems · Auction Theory and Applications · Distributed systems and fault tolerance
