22 research outputs found
Lower bounds on data collection time in sensory networks
Data collection, i.e., the aggregation at the user location of information gathered by sensor nodes, is a fundamental function of sensory networks. Indeed, most sensor network applications rely on data collection capabilities, and consequently, an inefficient data collection process may adversely affect the performance of the network. In this paper, we study via simple discrete mathematical models, the time performance of the data collection and data distribution tasks in sensory networks. Specifically, we derive the minimum delay in collecting sensor data for networks of various topologies such as line, multiline, and tree and give corresponding optimal scheduling strategies. Furthermore, we bound the data collection time on general graph networks. Our analyses apply to networks equipped with directional or omnidirectional antennas and simple comparative results of the two systems are presented
Near-linear Time Algorithm for Approximate Minimum Degree Spanning Trees
Given a graph , we wish to compute a spanning tree whose maximum
vertex degree, i.e. tree degree, is as small as possible. Computing the exact
optimal solution is known to be NP-hard, since it generalizes the Hamiltonian
path problem. For the approximation version of this problem, a
time algorithm that computes a spanning tree of degree at most is
previously known [F\"urer \& Raghavachari 1994]; here denotes the
minimum tree degree of all the spanning trees. In this paper we give the first
near-linear time approximation algorithm for this problem. Specifically
speaking, we propose an time algorithm that
computes a spanning tree with tree degree for any constant .
Thus, when , we can achieve approximate solutions with
constant approximate ratio arbitrarily close to 1 in near-linear time.Comment: 17 page
Bicriteria Network Design Problems
We study a general class of bicriteria network design problems. A generic
problem in this class is as follows: Given an undirected graph and two
minimization objectives (under different cost functions), with a budget
specified on the first, find a <subgraph \from a given subgraph-class that
minimizes the second objective subject to the budget on the first. We consider
three different criteria - the total edge cost, the diameter and the maximum
degree of the network. Here, we present the first polynomial-time approximation
algorithms for a large class of bicriteria network design problems for the
above mentioned criteria. The following general types of results are presented.
First, we develop a framework for bicriteria problems and their
approximations. Second, when the two criteria are the same %(note that the cost
functions continue to be different) we present a ``black box'' parametric
search technique. This black box takes in as input an (approximation) algorithm
for the unicriterion situation and generates an approximation algorithm for the
bicriteria case with only a constant factor loss in the performance guarantee.
Third, when the two criteria are the diameter and the total edge costs we use a
cluster-based approach to devise a approximation algorithms --- the solutions
output violate both the criteria by a logarithmic factor. Finally, for the
class of treewidth-bounded graphs, we provide pseudopolynomial-time algorithms
for a number of bicriteria problems using dynamic programming. We show how
these pseudopolynomial-time algorithms can be converted to fully
polynomial-time approximation schemes using a scaling technique.Comment: 24 pages 1 figur
Parameterized Complexity of Broadcasting in Graphs
The task of the broadcast problem is, given a graph G and a source vertex s,
to compute the minimum number of rounds required to disseminate a piece of
information from s to all vertices in the graph. It is assumed that, at each
round, an informed vertex can transmit the information to at most one of its
neighbors. The broadcast problem is known to NP-hard. We show that the problem
is FPT when parametrized by the size k of a feedback edge-set, or by the size k
of a vertex-cover, or by k=n-t where t is the input deadline for the broadcast
protocol to complete.Comment: Full version of WG 2023 pape
Polynomial-Time Space-Optimal Silent Self-Stabilizing Minimum-Degree Spanning Tree Construction
Motivated by applications to sensor networks, as well as to many other areas,
this paper studies the construction of minimum-degree spanning trees. We
consider the classical node-register state model, with a weakly fair scheduler,
and we present a space-optimal \emph{silent} self-stabilizing construction of
minimum-degree spanning trees in this model. Computing a spanning tree with
minimum degree is NP-hard. Therefore, we actually focus on constructing a
spanning tree whose degree is within one from the optimal. Our algorithm uses
registers on bits, converges in a polynomial number of rounds, and
performs polynomial-time computation at each node. Specifically, the algorithm
constructs and stabilizes on a special class of spanning trees, with degree at
most . Indeed, we prove that, unless NP coNP, there are no
proof-labeling schemes involving polynomial-time computation at each node for
the whole family of spanning trees with degree at most . Up to our
knowledge, this is the first example of the design of a compact silent
self-stabilizing algorithm constructing, and stabilizing on a subset of optimal
solutions to a natural problem for which there are no time-efficient
proof-labeling schemes. On our way to design our algorithm, we establish a set
of independent results that may have interest on their own. In particular, we
describe a new space-optimal silent self-stabilizing spanning tree
construction, stabilizing on \emph{any} spanning tree, in rounds, and
using just \emph{one} additional bit compared to the size of the labels used to
certify trees. We also design a silent loop-free self-stabilizing algorithm for
transforming a tree into another tree. Last but not least, we provide a silent
self-stabilizing algorithm for computing and certifying the labels of a
NCA-labeling scheme
Computation-Aware Data Aggregation
Data aggregation is a fundamental primitive in distributed computing wherein a network computes a function of every nodes\u27 input. However, while compute time is non-negligible in modern systems, standard models of distributed computing do not take compute time into account. Rather, most distributed models of computation only explicitly consider communication time.
In this paper, we introduce a model of distributed computation that considers both computation and communication so as to give a theoretical treatment of data aggregation. We study both the structure of and how to compute the fastest data aggregation schedule in this model. As our first result, we give a polynomial-time algorithm that computes the optimal schedule when the input network is a complete graph. Moreover, since one may want to aggregate data over a pre-existing network, we also study data aggregation scheduling on arbitrary graphs. We demonstrate that this problem on arbitrary graphs is hard to approximate within a multiplicative 1.5 factor. Finally, we give an O(log n ? log(OPT/t_m))-approximation algorithm for this problem on arbitrary graphs, where n is the number of nodes and OPT is the length of the optimal schedule
Minimal contention-free matrices with application to multicasting
In this paper, we show that the multicast problem in trees can be
expressed in term of arranging rows and columns of boolean matrices.
Given a matrix with 0-1 entries, the {\em shadow}
of is defined as a boolean vector of entries such that
if and only if there is no 1-entry in the th column of
, and otherwise. (The shadow can also be seen as the
binary expression of the integer .
Similarly, every row of can be seen as the binary expression of
an integer.) According to this formalism, the key for solving a
multicast problem in trees is shown to be the following. Given a matrix with 0-1 entries, finding a matrix such
that:
1- has at most one 1-entry per column;
2- every row of (viewed as the binary expression of
an integer) is larger than the corresponding row of , ; and
3- the shadow of (viewed as an integer) is minimum.
We show that there is an algorithm that
returns for any boolean matrix .
The application of this result is the following: Given a {\em directed}
tree whose arcs are oriented from the root toward the leaves,
and a subset of nodes , there exists a polynomial-time algorithm
that computes an optimal multicast protocol from the root to all
nodes of in the all-port line model.Peer Reviewe
Cross-layer schemes for performance optimization in wireless networks
Wireless networks are undergoing rapid progress and inspiring numerous applications. As the application of wireless networks becomes broader, they are expected to not only provide ubiquitous connectivity, but also support end users with certain service guarantees.
End-to-end delay is an important Quality of Service (QoS) metric in multihop wireless networks. This dissertation addresses how to minimize end-to-end delay through joint optimization of network layer routing and link layer scheduling. Two cross-layer schemes, a loosely coupled cross-layer scheme and a tightly coupled cross-layer scheme, are proposed. The two cross-layer schemes involve interference modeling in multihop wireless networks with omnidirectional antenna. In addition, based on the interference model, multicast schedules are optimized to minimize the total end-to-end delay.
Throughput is another important QoS metric in wireless networks. This dissertation addresses how to leverage the spatial multiplexing function of MIMO links to improve wireless network throughput. Wireless interference modeling of a half-duplex MIMO node is presented. Based on the interference model, routing, spatial multiplexing, and scheduling are jointly considered in one optimization model. The throughput optimization problem is first addressed in constant bit rate networks and then in variable bit rate networks. In a variable data rate network, transmitters can use adaptive coding and modulation schemes to change their data rates so that the data rates are supported by the Signal to Noise and Interference Ratio (SINR). The problem of achieving maximum throughput in a millimeter-wave wireless personal area network is studied --Abstract, page iv