arXiv subjects

Sebastian Senge

Publications and source records attributed to Sebastian Senge.

4 recordsLinked to original sources

arXiv2026

Exact Shortest Paths and Maximum Flow in Planar Networks in the CONGEST Model

In the CONGEST model, exact single-source shortest paths (SSSP) with nonnegative weights and exact maximum $st$-flow in directed planar networks have both been solved in $\tilde O(D^2)$ rounds, where $D$ is the hop diameter, while the lower bound is $Ω(D)$. Given the approximate distance labels of a recent preprint (arXiv:2606.31192), which we use as a black box, we solve exact directed SSSP in $\tilde O(D)$ rounds. It rests on a lemma that answers queries from a virtual source with the labels, and on a corrected discretization of the reduction of exact to approximate distances (arXiv:2210.16351). All further bounds of the form $\tilde O(D)$ and $D\cdot n^{o(1)}$ use these labels. Through the reduction of arXiv:2303.00811, SSSP with negative weights, or the detection of a negative cycle, takes $D\cdot n^{o(1)}$ rounds with high probability. We weight the face-disjoint graph of arXiv:2411.11718 so that its distances are dual distances, which turns distance problems in the dual into problems in a planar network of hop diameter $O(D)$. This gives exact maximum $st$-flow in directed planar networks in $\min\{\tilde O(D^2),D\cdot n^{o(1)}\}$ rounds with high probability, and in $\tilde O(D)$ rounds with $s,t$ on a common face. In undirected planar networks, the value of a minimum $st$-cut and a minimum cut take $\tilde O(D)$ rounds. For this we repair the auxiliary graphs of arXiv:2608.09500 at $s$ and $t$, and we show that its recursion, as we read it, can miss the minimum cut, also with exact shortest paths: on a network with $11$ vertices it reports $37$ for a minimum cut of $15$. Two more shortest-path computations per level make it exact. The virtual-source lemma, the weighting of the face-disjoint graph and the corrected discretization are machine-checked in Lean 4 with Mathlib; all other arguments are proved on paper only. Numerical checks are not used in any proof.

cs.DC↗

arXiv2026

Random Centres and the $\varepsilon$-Dependence of Constant-Round Planar Domination

It was recently shown (arXiv:2610.09618) that the infimum of the approximation ratios of deterministic constant-round LOCAL algorithms for minimum dominating set on planar graphs is 7. The $(7+\varepsilon)$-approximation given there runs in $T_0+O((c_0/\varepsilon)^κ)$ rounds with $κ=\ln 3/\ln(24/23)\approx 25.81$, and it is asked there whether this exponent can be substantially reduced. We replace the heaviest-edge star selection in its clustering step by a random-centre rule: every part becomes a centre independently with probability $p$, and every non-centre joins its heaviest centre neighbour. For planar graphs this gives $κ<5.89$ with $p=3/8$ (three fair coins per part and level) and $κ<6.7$ with $p=1/2$. An analysis that counts only the join edges cannot go below $5.74$. For every proper minor-closed class of density $a$, the new exponent is never worse, and with about $\frac12\log_2 a$ fair coins per part and level it is smaller by a factor that tends to $8$ as the density grows. This is optimal for the rule when $a$ is an integer and the class contains all $K_{a,n}$. The planar bounds hold verbatim on the torus, the projective plane and the Klein bottle. We then turn to the dependence on $\varepsilon$. On paths, every deterministic $r$-round algorithm for fractional domination, and every randomized one that always outputs a dominating set, has (expected) ratio at least $1+1/(r+4)$. So these approximations need $Ω(1/\varepsilon)$ rounds on every minor-closed class that contains all paths, and on paths this is tight up to an additive constant. On forests and on outerplanar graphs, with no bound on the degree, $O(1/\varepsilon)$ rounds suffice, so there the optimal number of rounds is $Θ(1/\varepsilon)$. The planar level bounds, the bounds on paths and the deterministic bound on forests are machine-checked in Lean 4 with Mathlib.

cs.DC↗

arXiv2026

A Connectome Test of the Fly Hashing Algorithm

Dasgupta, Stevens and Navlakha (2017) showed that the Drosophila olfactory circuit, modelled as a random sparse projection followed by winner-take-all, is a locality-sensitive hash that beats classical LSH. The projection was random because the wiring was unknown. We test it against four electron-microscopy connectomes (MaleCNS, hemibrain, FlyWire, BANC; four animals, seven hemispheres). First, the 2017 pattern holds in a reimplementation of its protocol on SIFT, MNIST and odour mixtures (GloVe is near chance at short codes for every method): the fly hash beats k Gaussian projections at short hash lengths (3.1x in AP@200 on MNIST at k = 4). Second, against the tested real-valued Gaussian baseline that advantage is per active cell, not per operation: Gaussian projections given the same projection arithmetic retrieve better on every dataset and input dimension tested. Third, across four connectomes the measured pairing of glomeruli gives no consistent retrieval advantage over degree-preserving rewiring: retrieval is slightly lower (median -1.6%), and the small odour deficits depend on how missing odour responses are treated. Separately, equalising glomerular fan-out at fixed connection count improves retrieval in the model in every hemisphere, while equalising inputs per cell lowers it on average. Yet the fan-out profile is similar across the four sampled animals (median between-animal Spearman rho = 0.86), structural synapse counts do not offset it, and its relation to odour tuning is weak. In the model that uneven allocation costs retrieval. For practice: measured wiring gives no consistent retrieval advantage over degree-preserving random wiring, so a fly hash needs no connectome data, and its advantage is per active unit, which may suit hardware where active units rather than arithmetic are the binding cost, a hypothesis we do not test.

cs.NE↗

arXiv2013

Assessment of Path Reservation in Distributed Real-Time Vehicle Guidance

In this paper we assess the impact of path reservation as an additional feature in our distributed real-time vehicle guidance protocol BeeJamA. Through our microscopic simulations we show that na\"ıve reservation of links without any further measurements is only an improvement in case of complete market penetration, otherwise it even reduces the performance of our approach based on real-time link loads. Moreover, we modified the reservation process to incorporate current travel times and show that this improves the results in our simulations when at least 40% market penetration is possible.

cs.MA↗