arXiv subjects

Stefan Neubert

Publications and source records attributed to Stefan Neubert.

4 recordsLinked to original sources

arXiv2025

Cost-Free Neutrality for the River Method

Recently, the River Method was introduced as novel refinement of the Split Cycle voting rule. The decision-making process of River is closely related to the well established Ranked Pairs Method. Both methods consider a margin graph computed from the voters' preferences and eliminate majority cycles in that graph to choose a winner. As ties can occur in the margin graph, a tiebreaker is required along with the preferences. While such a tiebreaker makes the computation efficient, it compromises the fundamental property of neutrality: the voting rule should not favor alternatives in advance. One way to reintroduce neutrality is to use Parallel-Universe Tiebreaking (PUT), where each alternative is a winner if it wins according to any possible tiebreaker. Unfortunately, computing the winners selected by Ranked Pairs with PUT is NP-complete. Given the similarity of River to Ranked Pairs, one might expect River to suffer from the same complexity. Surprisingly, we show the opposite: We present a polynomial-time algorithm for computing River winners with PUT, highlighting significant structural advantages of River over Ranked Pairs. Our Fused-Universe (FUN) algorithm simulates River for every possible tiebreaking in one pass. From the resulting FUN diagram one can then directly read off both the set of winners and, for each winner, a certificate that explains how this alternative dominates the others.

cs.DS↗

arXiv2025

Emit As You Go: Enumerating Edges of a Spanning Tree

Classically, planning tasks are studied as a two-step process: plan creation and plan execution. In situations where plan creation is slow (for example, due to expensive information access or complex constraints), a natural speed-up tactic is interleaving planning and execution. We implement such an approach with an enumeration algorithm that, after little preprocessing time, outputs parts of a plan one by one with little delay in-between consecutive outputs. As concrete planning task, we consider efficient connectivity in a network formalized as the minimum spanning tree problem in all four standard variants: (un)weighted (un)directed graphs. Solution parts to be emitted one by one for this concrete task are the individual edges that form the final tree. We show with algorithmic upper bounds and matching unconditional adversary lower bounds that efficient enumeration is possible for three of four problem variants; specifically for undirected unweighted graphs (delay in the order of the average degree), as well as graphs with either weights (delay in the order of the maximum degree and the average runtime per emitted edge of a total-time algorithm) or directions (delay in the order of the maximum degree). For graphs with both weighted and directed edges, we show that no meaningful enumeration is possible. Finally, with experiments on random undirected unweighted graphs, we show that the theoretical advantage of little preprocessing and delay carries over to practice.

cs.DS↗

arXiv2020

Shortest Distances as Enumeration Problem

We investigate the single source shortest distance (SSSD) and all pairs shortest distance (APSD) problems as enumeration problems (on unweighted and integer weighted graphs), meaning that the elements $(u, v, d(u, v))$ -- where $u$ and $v$ are vertices with shortest distance $d(u, v)$ -- are produced and listed one by one without repetition. The performance is measured in the RAM model of computation with respect to preprocessing time and delay, i.e., the maximum time that elapses between two consecutive outputs. This point of view reveals that specific types of output (e.g., excluding the non-reachable pairs $(u, v, \infty)$, or excluding the self-distances $(u, u, 0)$) and the order of enumeration (e.g., sorted by distance, sorted row-wise with respect to the distance matrix) have a huge impact on the complexity of APSD while they appear to have no effect on SSSD. In particular, we show for APSD that enumeration without output restrictions is possible with delay in the order of the average degree. Excluding non-reachable pairs, or requesting the output to be sorted by distance, increases this delay to the order of the maximum degree. Further, for weighted graphs, a delay in the order of the average degree is also not possible without preprocessing or considering self-distances as output. In contrast, for SSSD we find that a delay in the order of the maximum degree without preprocessing is attainable and unavoidable for any of these requirements.

cs.DS↗

arXiv2017

Efficient Best-Response Computation for Strategic Network Formation under Attack

Inspired by real world examples, e.g. the Internet, researchers have introduced an abundance of strategic games to study natural phenomena in networks. Unfortunately, almost all of these games have the conceptual drawback of being computationally intractable, i.e. computing a best response strategy or checking if an equilibrium is reached is NP-hard. Thus, a main challenge in the field is to find tractable realistic network formation models. We address this challenge by investigating a very recently introduced model by Goyal et al. [WINE'16] which focuses on robust networks in the presence of a strong adversary who attacks (and kills) nodes in the network and lets this attack spread virus-like to neighboring nodes and their neighbors. Our main result is to establish that this natural model is one of the few exceptions which are both realistic and computationally tractable. In particular, we answer an open question of Goyal et al. by providing an efficient algorithm for computing a best response strategy, which implies that deciding whether the game has reached a Nash equilibrium can be done efficiently as well. Our algorithm essentially solves the problem of computing a minimal connection to a network which maximizes the reachability while hedging against severe attacks on the network infrastructure and may thus be of independent interest.

cs.GT↗