Yannic Maus

Greedy Routing and the Algorithmic Small-World Phenomenon

The algorithmic small-world phenomenon, empirically established by Milgrams letter forwarding experiments from the 60s, was theoretically explained by Kleinberg in 2000. However, from todays perspective his model has several severe shortcomings that limit the applicability to real-world networks. In order to give a more convincing explanation of the algorithmic small-world phenomenon, we study decentralized greedy routing in a more flexible random graph model (geometric inhomogeneous random graphs) which overcomes all previous shortcomings. Apart from exhibiting good properties in theory, it has also been extensively experimentally validated that this model reasonably captures real-world networks. In this model, the greedy routing protocol is purely distributed as each vertex only needs to know information about its direct neighbors. We prove that it succeeds with constant probability, and in case of success almost surely finds an almost shortest path of length Θ(log log n), where our bound is tight including the leading constant. Moreover, we study natural local patching methods which augment greedy routing by backtracking and which do not require any global knowledge. We show that such methods can ensure success probability 1 in an asymptotically tight number of steps. These results also address the question of Krioukov et al. whether there are efficient local routing protocols for the internet graph. There were promising experimental studies, but the question remained unsolved theoretically. Our results give for the first time a rigorous and analytical affirmative answer.

Polynomial Lower Bound for Distributed Graph Coloring in a Weak LOCAL Model

We show an \(\varOmega \big (\varDelta ^{\frac{1}{3}-\frac{\eta }{3}}\big )\) lower bound on the runtime of any deterministic distributed \(\mathcal {O}\big (\varDelta ^{1+\eta }\big )\)-graph coloring algorithm in a weak variant of the \(\mathsf {LOCAL}\) model.

Deterministic distributed edge-coloring with fewer colors

We present a deterministic distributed algorithm, in the LOCAL model, that computes a (1+o(1))Δ-edge-coloring in polylogarithmic-time, so long as the maximum degree Δ=Ω(logn). For smaller Δ, we give a polylogarithmic-time 3Δ/2-edge-coloring. These are the first deterministic algorithms to go below the natural barrier of 2Δ−1 colors, and they improve significantly on the recent polylogarithmic-time (2Δ−1)(1+o(1))-edge-coloring of Ghaffari and Su [SODA’17] and the (2Δ−1)-edge-coloring of Fischer, Ghaffari, and Kuhn [FOCS’17], positively answering the main open question of the latter. The key technical ingredient of our algorithm is a simple and novel gradual packing of judiciously chosen near-maximum matchings, each of which becomes one of the color classes.

DISC 2017 Review

The 31st International Symposium on Distributed Computing, DISC 2017, was held on October 16-20, 2017, in Vienna, Austria. The main conference took place at the Austria Trend Hotel Park Royal Palace close to the Schönbrunn Castle. Many of the attendees claimed that they had not been to Vienna before, and, besides the conference events, also enjoyed visiting the city. However, attendance at all talks and the six (!) colocated workshops was very high. Many will remember this conference also for the great sweets and cakes that were served; there was probably no single person who did not go through some kind of a sugar shock. This review contains a few selected events and talks which constitute our personal highlights of the conference.