66 research outputs found
Local Approximation Schemes for Ad Hoc and Sensor Networks
We present two local approaches that yield polynomial-time approximation schemes (PTAS) for the Maximum Independent Set and Minimum Dominating Set problem in unit disk graphs. The algorithms run locally in each node and compute a (1+ε)-approximation to the problems at hand for any given ε > 0. The time complexity of both algorithms is O(TMIS + log*! n/εO(1)), where TMIS is the time required to compute a maximal independent set in the graph, and n denotes the number of nodes. We then extend these results to a more general class of graphs in which the maximum number of pair-wise independent nodes in every r-neighborhood is at most polynomial in r. Such graphs of polynomially bounded growth are introduced as a more realistic model for wireless networks and they generalize existing models, such as unit disk graphs or coverage area graphs
A Super-Fast Distributed Algorithm for Bipartite Metric Facility Location
The \textit{facility location} problem consists of a set of
\textit{facilities} , a set of \textit{clients} , an
\textit{opening cost} associated with each facility , and a
\textit{connection cost} between each facility and client
. The goal is to find a subset of facilities to \textit{open}, and to
connect each client to an open facility, so as to minimize the total facility
opening costs plus connection costs. This paper presents the first
expected-sub-logarithmic-round distributed O(1)-approximation algorithm in the
model for the \textit{metric} facility location problem on
the complete bipartite network with parts and . Our
algorithm has an expected running time of rounds, where . This result can be viewed as a continuation
of our recent work (ICALP 2012) in which we presented the first
sub-logarithmic-round distributed O(1)-approximation algorithm for metric
facility location on a \textit{clique} network. The bipartite setting presents
several new challenges not present in the problem on a clique network. We
present two new techniques to overcome these challenges. (i) In order to deal
with the problem of not being able to choose appropriate probabilities (due to
lack of adequate knowledge), we design an algorithm that performs a random walk
over a probability space and analyze the progress our algorithm makes as the
random walk proceeds. (ii) In order to deal with a problem of quickly
disseminating a collection of messages, possibly containing many duplicates,
over the bipartite network, we design a probabilistic hashing scheme that
delivers all of the messages in expected- rounds.Comment: 22 pages. This is the full version of a paper that appeared in DISC
201
Cost-aware compressive sensing for networked sensing systems
Compressive Sensing is a technique that can help reduce the sampling rate of sensing tasks. In mobile crowdsensing applications or wireless sensor networks, the resource burden of collecting samples is often a major concern. Therefore, compressive sensing is a promising approach in such scenarios. An implicit assumption underlying compressive sensing - both in theory and its applications - is that every sample has the same cost: its goal is to simply reduce the number of samples while achieving a good recovery accuracy. In many networked sensing systems, however, the cost of obtaining a specific sample may depend highly on the location, time, condition of the device, and many other factors of the sample. In this paper, we study compressive sensing in situations where different samples have different costs, and we seek to find a good trade-off between minimizing the total sample cost and the resulting recovery accuracy. We design CostAware Compressive Sensing (CACS), which incorporates the cost-diversity of samples into the compressive sensing framework, and we apply CACS in networked sensing systems. Technically, we use regularized column sum (RCS) as a predictive metric for recovery accuracy, and use this metric to design an optimization algorithm for finding a least cost randomized sampling scheme with provable recovery bounds. We also show how CACS can be applied in a distributed context. Using traffic monitoring and air pollution as concrete application examples, we evaluate CACS based on large-scale real-life traces. Our results show that CACS achieves significant cost savings, outperforming natural baselines (greedy and random sampling) by up to 4x
More with less: Lowering user burden in mobile crowdsourcing through compressive sensing
Mobile crowdsourcing is a powerful tool for collecting data of various types. The primary bottleneck in such systems is the high burden placed on the user who must manually collect sensor data or respond in-situ to simple queries (e.g., experience sampling studies). In this work, we present Compressive CrowdSensing (CCS) - a framework that enables compressive sensing techniques to be applied to mobile crowdsourcing scenarios. CCS enables each user to provide significantly reduced amounts of manually collected data, while still maintaining acceptable levels of overall accuracy for the target crowd-based system. Näive applications of compressive sensing do not work well for common types of crowdsourcing data (e.g., user survey responses) because the necessary correlations that are exploited by a sparsifying base are hidden and non-Trivial to identify. CCS comprises a series of novel techniques that enable such challenges to be overcome. We evaluate CCS with four representative large-scale datasets and find that it is able to outperform standard uses of compressive sensing, as well as conventional approaches to lowering the quantity of user data needed by crowd systems
Is Our Model for Contention Resolution Wrong?
Randomized binary exponential backoff (BEB) is a popular algorithm for
coordinating access to a shared channel. With an operational history exceeding
four decades, BEB is currently an important component of several wireless
standards. Despite this track record, prior theoretical results indicate that
under bursty traffic (1) BEB yields poor makespan and (2) superior algorithms
are possible. To date, the degree to which these findings manifest in practice
has not been resolved.
To address this issue, we examine one of the strongest cases against BEB:
packets that simultaneously begin contending for the wireless channel. Using
Network Simulator 3, we compare against more recent algorithms that are
inspired by BEB, but whose makespan guarantees are superior. Surprisingly, we
discover that these newer algorithms significantly underperform. Through
further investigation, we identify as the culprit a flawed but common
abstraction regarding the cost of collisions. Our experimental results are
complemented by analytical arguments that the number of collisions -- and not
solely makespan -- is an important metric to optimize. We believe that these
findings have implications for the design of contention-resolution algorithms.Comment: Accepted to the 29th ACM Symposium on Parallelism in Algorithms and
Architectures (SPAA 2017
Statistical Mechanics of maximal independent sets
The graph theoretic concept of maximal independent set arises in several
practical problems in computer science as well as in game theory. A maximal
independent set is defined by the set of occupied nodes that satisfy some
packing and covering constraints. It is known that finding minimum and
maximum-density maximal independent sets are hard optimization problems. In
this paper, we use cavity method of statistical physics and Monte Carlo
simulations to study the corresponding constraint satisfaction problem on
random graphs. We obtain the entropy of maximal independent sets within the
replica symmetric and one-step replica symmetry breaking frameworks, shedding
light on the metric structure of the landscape of solutions and suggesting a
class of possible algorithms. This is of particular relevance for the
application to the study of strategic interactions in social and economic
networks, where maximal independent sets correspond to pure Nash equilibria of
a graphical game of public goods allocation
Synchronous counting and computational algorithm design
Consider a complete communication network on n nodes, each of which is a state machine with s states. In synchronous 2-counting, the nodes receive a common clock pulse and they have to agree on which pulses are “odd” and which are “even”. We require that the solution is self-stabilising (reaching the correct operation from any initial state) and it tolerates f Byzantine failures (nodes that send arbitrary misinformation). Prior algorithms are expensive to implement in hardware: they require a source of random bits or a large number of states s. We use computational techniques to construct very compact deterministic algorithms for the first non-trivial case of f = 1. While no algorithm exists for n < 4, we show that as few as 3 states are sufficient for all values n ≥ 4. We prove that the problem cannot be solved with only 2 states for n = 4, but there is a 2-state solution for all values n ≥ 6.Peer reviewe
The Emergence of Sparse Spanners and Greedy Well-Separated Pair Decomposition
A spanner graph on a set of points in contains a shortest path between
any pair of points with length at most a constant factor of their Euclidean
distance. In this paper we investigate new models and aim to interpret why good
spanners 'emerge' in reality, when they are clearly built in pieces by agents
with their own interests and the construction is not coordinated. Our main
result is to show that if edges are built in an arbitrary order but an edge is
built if and only if its endpoints are not 'close' to the endpoints of an
existing edge, the graph is a (1 + \eps)-spanner with a linear number of
edges, constant average degree, and the total edge length as a small
logarithmic factor of the cost of the minimum spanning tree. As a side product,
we show a simple greedy algorithm for constructing optimal size well-separated
pair decompositions that may be of interest on its own
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