76 research outputs found
External inverse pattern matching
We consider {\sl external inverse pattern matching} problem. Given a text \t of length over an ordered alphabet , such that , and a number . The entire problem is to find a pattern \pe\in \Sigma^m which is not a subword of \t and which maximizes the sum of Hamming distances between \pe and all subwords of \t of length . We present optimal -time algorithm for the external inverse pattern matching problem which substantially improves the only known polynomial -time algorithm introduced by Amir, Apostolico and Lewenstein. Moreover we discuss a fast parallel implementation of our algorithm on the CREW PRAM model
Ephemeral networks with random availability of links: diameter and connectivity
In this work we consider temporal networks, the links of which are available only at random times (randomly available temporal networks). Our networks are {\em ephemeral}: their links appear sporadically, only at certain times, within a given maximum time (lifetime of the net). More specifically, our temporal networks notion concerns networks, whose edges (arcs) are assigned one or more random discrete-time labels drawn from a set of natural numbers. The labels of an edge indicate the discrete moments in time at which the edge is available. In such networks, information (e.g., messages) have to follow temporal paths, i.e., paths, the edges of which are assigned a strictly increasing sequence of labels. We first examine a very hostile network: a clique, each edge of which is known to be available only one random time in the time period {1,2, ..., n} (n is the number of vertices). How fast can a vertex send a message to all other vertices in such a network? To answer this, we define the notion of the Temporal Diameter for the random temporal clique and prove that it is Θ(log n) with high probability and in expectation. In fact, we show that information dissemination is very fast with high probability even in this hostile network with regard to availability. This result is similar to the results for the random phone-call model. Our model, though, is weaker. Our availability assumptions are different and randomness is provided only by the input. We show here that the temporal diameter of the clique is crucially affected by the clique's lifetime, a, e.g., when a is asymptotically larger than the number of vertices, n, then the temporal diameter must be Ω(a/nlog n ). We, then, consider the least number, r, of random points in time at which an edge is available, in order to guarantee at least a temporal path between any pair of vertices of the network (notice that the clique is the only network for which just one instance of availability per edge, even non-random, suffices for this). We show that r is Ω(log n) even for some networks of diameter 2. Finally, we compare this cost to an (optimal) deterministic allocation of labels of availability that guarantees a temporal path between any pair of vertices. For this reason, we introduce the notion of the Price of Randomness and we show an upper bound for general networks
Fast Structuring of Radio Networks for Multi-Message Communications
We introduce collision free layerings as a powerful way to structure radio
networks. These layerings can replace hard-to-compute BFS-trees in many
contexts while having an efficient randomized distributed construction. We
demonstrate their versatility by using them to provide near optimal distributed
algorithms for several multi-message communication primitives.
Designing efficient communication primitives for radio networks has a rich
history that began 25 years ago when Bar-Yehuda et al. introduced fast
randomized algorithms for broadcasting and for constructing BFS-trees. Their
BFS-tree construction time was rounds, where is the network
diameter and is the number of nodes. Since then, the complexity of a
broadcast has been resolved to be rounds. On the other hand, BFS-trees have been used as a crucial building
block for many communication primitives and their construction time remained a
bottleneck for these primitives.
We introduce collision free layerings that can be used in place of BFS-trees
and we give a randomized construction of these layerings that runs in nearly
broadcast time, that is, w.h.p. in rounds for any constant . We then use these
layerings to obtain: (1) A randomized algorithm for gathering messages
running w.h.p. in rounds. (2) A randomized -message
broadcast algorithm running w.h.p. in rounds. These
algorithms are optimal up to the small difference in the additive
poly-logarithmic term between and . Moreover, they imply the
first optimal round randomized gossip algorithm
Deterministic Population Protocols for Exact Majority and Plurality
In this paper we study space-efficient deterministic population protocols for several variants of the majority problem including plurality consensus. We focus on space efficient majority protocols in populations with an arbitrary number of colours C represented by k-bit labels, where k = ceiling (log C). In particular, we present asymptotically space-optimal (with respect to the adopted k-bit representation of colours) protocols for (1) the absolute majority problem, i.e., a protocol which decides whether a single colour dominates all other colours considered together, and (2) the relative majority problem, also known in the literature as plurality consensus, in which colours declare their volume superiority versus other individual colours. The new population protocols proposed in this paper rely on a dynamic formulation of the majority problem in which the colours originally present in the population can be changed by an external force during the communication process. The considered dynamic formulation is based on the concepts studied by D. Angluin et al. and O. Michail et al. about stabilizing inputs and composition of population protocols. Also, the protocols presented in this paper use a composition of some known protocols for static and dynamic majority
When Patrolmen Become Corrupted: Monitoring a Graph Using Faulty Mobile Robots
A team of k mobile robots is deployed on a weighted graph whose edge weights represent distances. The robots move perpetually along the domain, represented by all points belonging to the graph edges, without exceeding their maximum speed. The robots need to patrol the graph by regularly visiting all points of the domain. In this paper, we consider a team of robots (patrolmen), at most f of which may be unreliable, i.e., they fail to comply with their patrolling duties. What algorithm should be followed so as to minimize the maximum time between successive visits of every edge point by a reliable patrolman? The corresponding measure of efficiency of patrolling called idleness has been widely accepted in the robotics literature. We extend it to the case of untrusted patrolmen; we denote by Ifk(G) the maximum time that a point of the domain may remain unvisited by reliable patrolmen. The objective is to find patrolling strategies minimizing Ifk(G). We investigate this problem for various classes of graphs. We design optimal algorithms for line segments, which turn out to be surprisingly different from strategies for related patrolling problems proposed in the literature. We then use these results to study general graphs. For Eulerian graphs G, we give an optimal patrolling strategy with idleness Ifk(G)=(f+1)|E|/k, where |E| is the sum of the lengths of the edges of G. Further, we show the hardness of the problem of computing the idle time for three robots, at most one of which is faulty, by reduction from 3-edge-coloring of cubic graphs—a known NP-hard problem. A byproduct of our proof is the investigation of classes of graphs minimizing idle time (with respect to the total length of edges); an example of such a class is known in the literature under the name of Kotzig graphs
Fault-Tolerant Aggregation: Flow-Updating Meets Mass-Distribution
Flow-Updating (FU) is a fault-tolerant technique that has proved to be
efficient in practice for the distributed computation of aggregate functions in
communication networks where individual processors do not have access to global
information. Previous distributed aggregation protocols, based on repeated
sharing of input values (or mass) among processors, sometimes called
Mass-Distribution (MD) protocols, are not resilient to communication failures
(or message loss) because such failures yield a loss of mass. In this paper, we
present a protocol which we call Mass-Distribution with Flow-Updating (MDFU).
We obtain MDFU by applying FU techniques to classic MD. We analyze the
convergence time of MDFU showing that stochastic message loss produces low
overhead. This is the first convergence proof of an FU-based algorithm. We
evaluate MDFU experimentally, comparing it with previous MD and FU protocols,
and verifying the behavior predicted by the analysis. Finally, given that MDFU
incurs a fixed deviation proportional to the message-loss rate, we adjust the
accuracy of MDFU heuristically in a new protocol called MDFU with Linear
Prediction (MDFU-LP). The evaluation shows that both MDFU and MDFU-LP behave
very well in practice, even under high rates of message loss and even changing
the input values dynamically.Comment: 18 pages, 5 figures, To appear in OPODIS 201
Fast Label Extraction in the CDAWG
The compact directed acyclic word graph (CDAWG) of a string of length
takes space proportional just to the number of right extensions of the
maximal repeats of , and it is thus an appealing index for highly repetitive
datasets, like collections of genomes from similar species, in which grows
significantly more slowly than . We reduce from to
the time needed to count the number of occurrences of a pattern of
length , using an existing data structure that takes an amount of space
proportional to the size of the CDAWG. This implies a reduction from
to in the time needed to
locate all the occurrences of the pattern. We also reduce from
to the time needed to read the characters of the
label of an edge of the suffix tree of , and we reduce from
to the time needed to compute the matching
statistics between a query of length and , using an existing
representation of the suffix tree based on the CDAWG. All such improvements
derive from extracting the label of a vertex or of an arc of the CDAWG using a
straight-line program induced by the reversed CDAWG.Comment: 16 pages, 1 figure. In proceedings of the 24th International
Symposium on String Processing and Information Retrieval (SPIRE 2017). arXiv
admin note: text overlap with arXiv:1705.0864
Information Gathering in Ad-Hoc Radio Networks with Tree Topology
We study the problem of information gathering in ad-hoc radio networks
without collision detection, focussing on the case when the network forms a
tree, with edges directed towards the root. Initially, each node has a piece of
information that we refer to as a rumor. Our goal is to design protocols that
deliver all rumors to the root of the tree as quickly as possible. The protocol
must complete this task within its allotted time even though the actual tree
topology is unknown when the computation starts. In the deterministic case,
assuming that the nodes are labeled with small integers, we give an O(n)-time
protocol that uses unbounded messages, and an O(n log n)-time protocol using
bounded messages, where any message can include only one rumor. We also
consider fire-and-forward protocols, in which a node can only transmit its own
rumor or the rumor received in the previous step. We give a deterministic
fire-and- forward protocol with running time O(n^1.5), and we show that it is
asymptotically optimal. We then study randomized algorithms where the nodes are
not labelled. In this model, we give an O(n log n)-time protocol and we prove
that this bound is asymptotically optimal
Gathering algorithms on paths under interference constraints
International audienceWe study the problem of gathering information from the nodes of a multi-hop radio network into a pre-determined destination node under interference constraints which are modeled by an integer d 1, so that any node within distance d of a sender cannot receive calls from any other sender. A set of calls which do not interfere with each other is referred to as a round. We give algorithms and lower bounds on the minimum number of rounds for this problem, when the network is a path and the destination node is either at one end or at the center of the path. The algorithms are shown to be optimal for any d in the rst case, and for 1 d 4, in the second case
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