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Christian Scheideler

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27 papers
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27

SODA Conference 2020 Conference Paper

Shortest Paths in a Hybrid Network Model

  • John Augustine 0001
  • Kristian Hinnenthal
  • Fabian Kuhn
  • Christian Scheideler
  • Philipp Schneider

We introduce a communication model for hybrid networks, where nodes have access to two different communication modes: a local mode where (like in traditional networks) communication is only possible between specific pairs of nodes, and a global mode where (like in overlay networks) communication between any pair of nodes is possible. Typically, communication over short-range connections is cheaper and can be done at a much higher rate than communication via the overlay network. Therefore, we are focusing on the LOCAL model for the local connections where nodes can exchange an unbounded amount of information per round. For the global communication we assume the so-called nodecapacitated clique model, where in each round every node can exchange O (log n )-bit messages with O (log n ) arbitrary nodes. We explore the impact of hybrid communication on the complexity of distributed algorithms by studying the problem of computing shortest paths in the graph given by the local connections. We present the following results. For the all-pairs shortest paths problem, we show that an exact solution can be computed in time Õ ( n 2/3 ), and that approximate solutions can be computed in time but not faster. For the single-source shortest paths problem an exact solution can be computed in time, where SPD denotes the shortest path diameter. Furthermore, a (l + o (1))-approximate solution can be computed in time. Finally, we show that for every constant ε > 0, it is possible to compute an O (1)-approximate solution in time.

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MFCS Conference 2018 Conference Paper

Shape Recognition by a Finite Automaton Robot

  • Robert Gmyr
  • Kristian Hinnenthal
  • Irina Kostitsyna
  • Fabian Kuhn
  • Dorian Rudolph
  • Christian Scheideler

Motivated by the problem of shape recognition by nanoscale computing agents, we investigate the problem of detecting the geometric shape of a structure composed of hexagonal tiles by a finite-state automaton robot. In particular, in this paper we consider the question of recognizing whether the tiles are assembled into a parallelogram whose longer side has length l = f(h), for a given function f(*), where h is the length of the shorter side. To determine the computational power of the finite-state automaton robot, we identify functions that can or cannot be decided when the robot is given a certain number of pebbles. We show that the robot can decide whether l = ah+b for constant integers a and b without any pebbles, but cannot detect whether l = f(h) for any function f(x) = omega(x). For a robot with a single pebble, we present an algorithm to decide whether l = p(h) for a given polynomial p(*) of constant degree. We contrast this result by showing that, for any constant k, any function f(x) = omega(x^(6k + 2)) cannot be decided by a robot with k states and a single pebble. We further present exponential functions that can be decided using two pebbles. Finally, we present a family of functions f_n(*) such that the robot needs more than n pebbles to decide whether l = f_n(h).

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STOC Conference 2005 Conference Paper

How to spread adversarial nodes? : rotate!

  • Christian Scheideler

In this paper we study the problem of how to keep a dynamic system of nodes well-mixed even under adversarial behavior. This problem is very important in the context of distributed systems.More specifically, we consider the following game: There are n white pebbles and ε n black pebbles for some fixed constant ε < 1. Initially, all of the white pebbles are laid down in a ring, and the adversary has all of the black pebbles in its bag. In each round, the adversary can look at the entire ring and can select to add a black pebble to the ring (if its bag is not empty) or to take any black pebble from the ring and put it back into its bag (i.e. we consider adaptive adversaries). However, the adversary cannot place a black pebble into any position it likes. This is handled by a join strategy to be specified by the system. The goal is to find an oblivious join strategy, i.e. a strategy that cannot distinguish between the white and black pebbles in the ring, that integrates the black pebbles into this ring and may do some further rearrangements so that for a polynomial number of rounds the adversary will not manage to include its black pebbles into the ring so that there is a sequence of s=Θ(log n) consecutive pebbles in which at least half of the pebbles are black. If this is achieved by the join strategy, it wins. Otherwise, the adversary wins.Of course, the brute-force strategy of rearranging all of the pebbles in the ring at random after each insertion of a black pebble will achieve the stated goal, with high probability, but this would be a very expensive strategy. The challenge is to find a join strategy that needs as little randomness and as few rearrangements as possible in order to win with high probability. In this paper, we present and analyze a very simple strategy called k-rotation that chooses k-1 existing positions uniformly at random in the ring, creates a new position uniformly at random in the ring, and then rotates the new pebble and the k-1 old pebbles along these positions. Interestingly, even if the adversary has just $s$ pebbles, it can still win for k=2. But the k-rotation rule wins with high probability for k=3 as long as ε<2/3, demonstrating that there is a sharp threshold for keeping pebbles in a sufficiently perturbed state.

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FOCS Conference 2001 Conference Paper

Simple Routing Strategies for Adversarial Systems

  • Baruch Awerbuch
  • Petra Berenbrink
  • André Brinkmann
  • Christian Scheideler

In this paper we consider the problem of delivering dynamically changing input streams in dynamically changing networks where both the topology and the input streams can change in an unpredictable way. In particular, we present two simple distributed balancing algorithms (one for packet injections and one for flow injections) and show that for the case of a single receiver these algorithms will always ensure that the number of packets or flow in the system is bounded at any time step, even for an injection process that completely saturates the capacities of the available edges and even if the network topology changes in a completely unpredictable way. We also show that the maximum number of packets or flow that can be in the system at any time is essentially best possible by providing a lower bound that holds for any online algorithm, whether distributed or not. Interestingly, our balancing algorithms do not behave well in a completely adversarial setting. We show that also in the other extreme of a static network and a static injection pattern the algorithms will converge to a point in which they achieve an average routing time that is close to the best possible average routing time that can be achieved by any strategy. This demonstrates that there are simple algorithms that can be efficient for very different scenarios.

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FOCS Conference 1996 Conference Paper

Deterministic Routing with Bounded Buffers: Turning Offline into Online Protocols

  • Friedhelm Meyer auf der Heide
  • Christian Scheideler

In this paper we present a deterministic protocol for routing arbitrary permutations in arbitrary networks. The protocol is analyzed in terms of the size of the network and the routing number of the network. Given a network H of size n, the routing number of H is defined as the maximum over all permutations /spl pi/ on [n] of the minimal number of steps to route /spl pi/ offline in H. We can show that for any network H of size n with routing number R our protocol needs O(log/sub R/ n/spl middot/R) time to route any permutation in H using only constant size edge buffers. This significantly improves all previously known results on deterministic routing. In particular our result yields optimal deterministic routing protocols for arbitrary networks with diameter /spl Omega/(n/sup /spl epsiv//) or bisection width O(n/sup 1-/spl epsiv//), /spl epsiv/>0 constant. Furthermore we can extend our result to deterministic compact routing. This yields, e. g. , a deterministic routing protocol with runtime O((log n)/(log log n) R) for arbitrary bounded degree networks if only O(log n) bits are available at each node for storing routing information. Our proofs use a new protocol for routing arbitrary r/spl middot/s-relations in r-replicated s-ary Multibutterflies in optimal time O(log, n).

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