TY - JOUR
AB - An elementary h-route ow, for an integer h 1, is a set of h edge- disjoint paths between a source and a sink, each path carrying a unit of ow, and an h-route ow is a non-negative linear combination of elementary h-routeows. An h-route cut is a set of edges whose removal decreases the maximum h-route ow between a given source-sink pair (or between every source-sink pair in the multicommodity setting) to zero. The main result of this paper is an approximate duality theorem for multicommodity h-route cuts and ows, for h 3: The size of a minimum h-route cut is at least f=h and at most O(log4 k f) where f is the size of the maximum h-routeow and k is the number of commodities. The main step towards the proof of this duality is the design and analysis of a polynomial-time approximation algorithm for the minimum h-route cut problem for h = 3 that has an approximation ratio of O(log4 k). Previously, polylogarithmic approximation was known only for h-route cuts for h 2. A key ingredient of our algorithm is a novel rounding technique that we call multilevel ball-growing. Though the proof of the duality relies on this algorithm, it is not a straightforward corollary of it as in the case of classical multicommodity ows and cuts. Similar results are shown also for the sparsest multiroute cut problem.
AU - Kolman, Petr
AU - Scheideler, Christian
ID - 476
IS - 2
JF - Theory of Computing Systems
TI - Towards Duality of Multicommodity Multiroute Cuts and Flows: Multilevel Ball-Growing
ER -
TY - JOUR
AU - Dolev, Shlomi
AU - Scheideler, Christian
ID - 1882
JF - Theor. Comput. Sci.
TI - Editorial for Algorithmic Aspects of Wireless Sensor Networks
ER -
TY - JOUR
AB - We present Tiara — a self-stabilizing peer-to-peer network maintenance algorithm. Tiara is truly deterministic which allows it to achieve exact performance bounds. Tiara allows logarithmic searches and topology updates. It is based on a novel sparse 0-1 skip list. We then describe its extension to a ringed structure and to a skip-graph.Key words: Peer-to-peer networks, overlay networks, self-stabilization.
AU - Clouser, Thomas
AU - Nesterenko, Mikhail
AU - Scheideler, Christian
ID - 574
JF - Theoretical Computer Science
TI - Tiara: A self-stabilizing deterministic skip list and skip graph
ER -
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 - 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
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
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 -