TY - JOUR
AB - A left-to-right maximum in a sequence of n numbers s_1, …, s_n is a number that is strictly larger than all preceding numbers. In this article we present a smoothed analysis of the number of left-to-right maxima in the presence of additive random noise. We show that for every sequence of n numbers s_i ∈ [0,1] that are perturbed by uniform noise from the interval [-ε,ε], the expected number of left-to-right maxima is Θ(&sqrt;n/ε + log n) for ε>1/n. For Gaussian noise with standard deviation σ we obtain a bound of O((log3/2 n)/σ + log n).We apply our results to the analysis of the smoothed height of binary search trees and the smoothed number of comparisons in the quicksort algorithm and prove bounds of Θ(&sqrt;n/ε + log n) and Θ(n/ε+1&sqrt;n/ε + n log n), respectively, for uniform random noise from the interval [-ε,ε]. Our results can also be applied to bound the smoothed number of points on a convex hull of points in the two-dimensional plane and to smoothed motion complexity, a concept we describe in this article. We bound how often one needs to update a data structure storing the smallest axis-aligned box enclosing a set of points moving in d-dimensional space.
AU - Damerow, Valentina
AU - Manthey, Bodo
AU - Meyer auf der Heide, Friedhelm
AU - Räcke, Harald
AU - Scheideler, Christian
AU - Sohler, Christian
AU - Tantau, Till
ID - 579
IS - 3
JF - Transactions on Algorithms
TI - Smoothed analysis of left-to-right maxima with applications
ER -
TY - CONF
AB - Nanoparticles are getting more and more in the focus of the scientic community since the potential for the development of very small particles interacting with each other and completing medical and other tasks is getting bigger year by year. In this work we introduce a distributed local algorithm for arranging a set of nanoparticles on the discrete plane into specic geometric shapes, for instance a rectangle. The concept of a particle we use can be seen as a simple mobile robot with the following restrictions: it can only view the state of robots it is physically connected to, is anonymous, has only a constant size memory, can only move by using other particles as an anchor point on which it pulls itself alongside, and it operates in Look-Compute-Move cycles. The main result of this work is the presentation of a random distributed local algorithm which transforms any given connected set of particles into a particular geometric shape. As an example we provide a version of this algorithm for forming a rectangle with an arbitrary predened aspect ratio. To the best of our knowledge this is the rst work that considers arrangement problems for these types of robots.
AU - Drees, Maximilian
AU - Hüllmann (married name: Eikel), Martina
AU - Koutsopoulos, Andreas
AU - Scheideler, Christian
ID - 581
T2 - Proceedings of the 26th IEEE International Parallel and Distributed Processing Symposium (IPDPS)
TI - Self-Organizing Particle Systems
ER -
TY - CONF
AB - This paper initiates the study of self-adjusting distributed data structures for networks. In particular, we present SplayNets: a binary search tree based network that is self-adjusting to routing request.We derive entropy bounds on the amortized routing cost and show that our splaying algorithm has some interesting properties.
AU - Schmid, Stefan
AU - Avin, Chen
AU - Scheideler, Christian
AU - Häupler, Bernhard
AU - Lotker, Zvi
ID - 625
T2 - Proceedings of the 26th International Symposium on Distributed Computing (DISC)
TI - Brief Announcement: SplayNets - Towards Self-Adjusting Distributed Data Structures
ER -
TY - CONF
AB - Given an integer h, a graph G = (V;E) with arbitrary positive edge capacities and k pairs of vertices (s1; t1); (s2; t2); : : : ; (sk; tk), called terminals, an h-route cut is a set F µ E of edges such that after the removal of the edges in F no pair si ¡ ti is connected by h edge-disjoint paths (i.e., the connectivity of every si ¡ ti pair is at most h ¡ 1 in (V;E n F)). The h-route cut is a natural generalization of the classical cut problem for multicommodity °ows (take h = 1). The main result of this paper is an O(h722h log2 k)-approximation algorithm for the minimum h-route cut problem in the case that s1 = s2 = ¢ ¢ ¢ = sk, called the single source case. As a corollary of it we obtain an approximate duality theorem for multiroute multicom-modity °ows and cuts with a single source. This partially answers an open question posted in several previous papers dealing with cuts for multicommodity multiroute problems.
AU - Kolman, Petr
AU - Scheideler, Christian
ID - 632
T2 - Proceedings of the 23th ACM SIAM Symposium on Discrete Algorithms (SODA)
TI - Approximate Duality of Multicommodity Multiroute Flows and Cuts: Single Source Case
ER -
TY - CONF
AU - Monien, Burkhard
AU - Scheideler, Christian
ID - 1884
SN - 978-3-642-32819-0
T2 - Euro-Par 2012 Parallel Processing - 18th International Conference, Euro-Par 2012, Rhodes Island, Greece, August 27-31, 2012. Proceedings
TI - Selfish Distributed Optimization
VL - 7484
ER -
TY - JOUR
AB - This article studies the construction of self-stabilizing topologies for distributed systems. While recent research has focused on chain topologies where nodes need to be linearized with respect to their identiers, we explore a natural and relevant 2-dimensional generalization. In particular, we present a local self-stabilizing algorithm DStab which is based on the concept of \local Delaunay graphs" and which forwards temporary edges in greedy fashion reminiscent of compass routing. DStab constructs a Delaunay graph from any initial connected topology and in a distributed manner in time O(n3) in the worst-case; if the initial network contains the Delaunay graph, the convergence time is only O(n) rounds. DStab also ensures that individual node joins and leaves aect a small part of the network only. Such self-stabilizing Delaunay networks have interesting applications and our construction gives insights into the necessary geometric reasoning that is required for higherdimensional linearization problems.Keywords: Distributed Algorithms, Topology Control, Social Networks
AU - Jacob, Riko
AU - Ritscher, Stephan
AU - Scheideler, Christian
AU - Schmid, Stefan
ID - 570
JF - Theoretical Computer Science
TI - Towards higher-dimensional topological self-stabilization: A distributed algorithm for Delaunay graphs
ER -
TY - CONF
AB - The design of ecient search structures for peer-to-peer systems has attracted a lot of attention in recent years. In this announcement we address the problem of nding the predecessor in a key set and present an ecient data structure called hashed Predecessor Patricia trie. Our hashed Predecessor Patricia trie supports PredecessorSearch(x) and Insert(x) and Delete(x) in O(log log u) hash table accesses when u is the size of the universe of the keys. That is the costs only depend on u and not the size of the data structure. One feature of our approach is that it only uses the lookup interface of the hash table and therefore hash table accesses may be realized by any distributed hash table (DHT).
AU - Kniesburges, Sebastian
AU - Scheideler, Christian
ID - 626
T2 - Proceedings of the 26th International Symposium on Distributed Computing (DISC)
TI - Brief Announcement: Hashed Predecessor Patricia Trie - A Data Structure for Efficient Predecessor Queries in Peer-to-Peer Systems
ER -
TY - CONF
AB - Small-world networks have received significant attention because of their potential as models for the interaction networks of complex systems. Specifically, neither random networks nor regular lattices seem to be an adequate framework within which to study real-world complex systems such as chemical-reaction networks, neural networks, food webs, social networks, scientific-collaboration networks, and computer networks. Small-world networks provide some desired properties like an expected polylogarithmic distance between two processes in the network, which allows routing in polylogarithmic hops by simple greedy routing, and robustness against attacks or failures. By these properties, small-world networks are possible solutions for large overlay networks comparable to structured overlay networks like CAN, Pastry, Chord, which also provide polylogarithmic routing, but due to their uniform structure, structured overlay networks are more vulnerable to attacks or failures. In this paper we bring together a randomized process converging to a small-world network and a self-stabilization process so that a small-world network is formed out of any weakly connected initial state. To the best of our knowledge this is the first distributed self-stabilization process for building a small-world network.
AU - Kniesburges, Sebastian
AU - Koutsopoulos, Andreas
AU - Scheideler, Christian
ID - 640
T2 - Proceedings of the 26th IEEE International Parallel and Distributed Processing Symposium (IPDPS)
TI - A Self-Stabilization Process for Small-World Networks
ER -
TY - CONF
AB - This paper initiates the formal study of a fundamental problem: How to efficiently allocate a shared communication medium among a set of K co-existing networks in the presence of arbitrary external interference? While most literature on medium access focuses on how to share a medium among nodes, these approaches are often either not directly applicable to co-existing networks as they would violate the independence requirement, or they yield a low throughput if applied to multiple networks. We present the randomized medium access (MAC) protocol COMAC which guarantees that a given communication channel is shared fairly among competing and independent networks, and that the available bandwidth is used efficiently. These performance guarantees hold in the presence of arbitrary external interference or even under adversarial jamming. Concretely, we show that the co-existing networks can use a Ω(ε2 min{ε, 1/poly(K)})-fraction of the non-jammed time steps for successful message transmissions, where ε is the (arbitrarily distributed) fraction of time which is not jammed.
AU - Richa, Andrea W.
AU - Scheideler, Christian
AU - Schmid, Stefan
AU - Zhang, Jin
ID - 623
T2 - Proceedings of the 31st Annual ACM SIGACT-SIGOPS Symposium on Principles and Distributed Computing (PODC)
TI - Competitive and fair throughput for co-existing networks under adversarial interference
ER -
TY - CONF
AU - Kniesburges, Sebastian
AU - Scheideler, Christian
ID - 1899
SN - 978-3-642-19093-3
T2 - WALCOM: Algorithms and Computation - 5th International Workshop, WALCOM 2011, New Delhi, India, February 18-20, 2011. Proceedings
TI - Hashed Patricia Trie: Efficient Longest Prefix Matching in Peer-to-Peer Systems
VL - 6552
ER -
TY - CONF
AB - We present Corona, a deterministic self-stabilizing algorithm for skip list construction in structured overlay networks. Corona operates in the low-atomicity message-passing asynchronous system model. Corona requires constant process memory space for its operation and, therefore, scales well. We prove the general necessary conditions limiting the initial states from which a self-stabilizing structured overlay network in message-passing system can be constructed. The conditions require that initial state information has to form a weakly connected graph and it should only contain identiers that are present in the system. We formally describe Corona and rigorously prove that it stabilizes from an arbitrary initial state subject to the necessary conditions. We extend Corona to construct a skip graph.
AU - Nesterenko, Mikhail
AU - Mohd, Rizal
AU - Scheideler, Christian
ID - 662
T2 - Proceedings of the 13th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS)
TI - Corona: A Stabilizing Deterministic Message-Passing Skip List
ER -
TY - CONF
AU - Kniesburges, Sebastian
AU - Koutsopoulos, Andreas
AU - Scheideler, Christian
ID - 1895
SN - 978-1-4503-0743-7
T2 - SPAA 2011: Proceedings of the 23rd Annual ACM Symposium on Parallelism in Algorithms and Architectures, San Jose, CA, USA, June 4-6, 2011 (Co-located with FCRC 2011)
TI - Re-Chord: a self-stabilizing chord overlay network
ER -
TY - CONF
AU - W. Richa, Andrea
AU - Scheideler, Christian
AU - Schmid, Stefan
AU - Zhang, Jin
ID - 1891
SN - 978-0-7695-4364-2
T2 - 2011 International Conference on Distributed Computing Systems, ICDCS 2011, Minneapolis, Minnesota, USA, June 20-24, 2011
TI - Competitive and Fair Medium Access Despite Reactive Jamming
ER -
TY - CONF
AB - In the standard consensus problem there are n processes with possibly di®erent input values and the goal is to eventually reach a point at which all processes commit to exactly one of these values. We are studying a slight variant of the consensus problem called the stabilizing consensus problem [2]. In this problem, we do not require that each process commits to a ¯nal value at some point, but that eventually they arrive at a common, stable value without necessarily being aware of that. This should work irrespective of the states in which the processes are starting. Our main result is a simple randomized algorithm called median rule that, with high probability, just needs O(logmlog log n + log n) time and work per process to arrive at an almost stable consensus for any set of m legal values as long as an adversary can corrupt the states of at most p n processes at any time. Without adversarial involvement, just O(log n) time and work is needed for a stable consensus, with high probability. As a by-product, we obtain a simple distributed algorithm for approximating the median of n numbers in time O(logmlog log n + log n) under adversarial presence.
AU - Doerr, Benjamin
AU - Goldberg, Leslie Ann
AU - Minder, Lorenz
AU - Sauerwald, Thomas
AU - Scheideler, Christian
ID - 645
T2 - Proceedings of the 23rd ACM Symposium on Parallelism in Algorithms and Architectures (SPAA)
TI - Stabilizing consensus with the power of two choices
ER -
TY - CONF
AU - W. Richa, Andrea
AU - Scheideler, Christian
AU - Schmid, Stefan
AU - Zhang, Jin
ID - 1892
SN - 978-1-4503-0868-7
T2 - Proceedings of the 3rd ACM workshop on Wireless of the students, by the students, for the students, S3@MOBICOM 2011, Las Vegas, NV, USA, September 19 - 23, 2011
TI - Towards jamming-resistant and competitive medium access in the SINR model
ER -
TY - CHAP
AU - Scheideler, Christian
AU - Graffi, Kalman
ID - 1900
SN - 978-1-4614-1167-3
T2 - Computer Science, The Hardware, Software and Heart of It
TI - Programming for Distributed Computing: From Physical to Logical Networks
ER -
TY - CONF
AU - Kolman, Petr
AU - Scheideler, Christian
ID - 1924
T2 - 28th International Symposium on Theoretical Aspects of Computer Science, STACS 2011, March 10-12, 2011, Dortmund, Germany
TI - Towards Duality of Multicommodity Multiroute Cuts and Flows: Multilevel Ball-Growing
ER -
TY - CONF
AB - This paper presents a dynamic overlay network based on the De Bruijn graph which we call Linearized De Bruijn (LDB) network. The LDB network has the advantage that it has a guaranteed constant node degree and that the routing between any two nodes takes at most O(log n) hops with high probability. Also, we show that there is a simple local-control algorithm that can recover the LDB network from any network topology that is weakly connected.
AU - Richa, Andrea W.
AU - Scheideler, Christian
ID - 646
T2 - Proceedings of the 13th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS)
TI - Self-Stabilizing DeBruijn Networks
ER -
TY - CONF
AU - W. Richa, Andrea
AU - Scheideler, Christian
AU - Schmid, Stefan
AU - Zhang, Jin
ID - 1893
SN - 978-1-4503-0722-2
T2 - Proceedings of the 12th ACM Interational Symposium on Mobile Ad Hoc Networking and Computing, MobiHoc 2011, Paris, France, May 16-20, 2011
TI - Self-stabilizing leader election for single-hop wireless networks despite jamming
ER -
TY - CHAP
AU - Scheideler, Christian
ID - 1901
SN - 978-3-642-15327-3
T2 - Algorithms Unplugged
TI - Broadcasting - How Can I Quickly Disseminate Information?
ER -