25,205 research outputs found
Improved Approximation Algorithms for Computing k Disjoint Paths Subject to Two Constraints
For a given graph with positive integral cost and delay on edges,
distinct vertices and , cost bound and delay bound , the bi-constraint path (BCP) problem is to compute disjoint
-paths subject to and . This problem is known NP-hard, even when
\cite{garey1979computers}. This paper first gives a simple approximation
algorithm with factor-, i.e. the algorithm computes a solution with
delay and cost bounded by and respectively. Later, a novel improved
approximation algorithm with ratio
is developed by constructing
interesting auxiliary graphs and employing the cycle cancellation method. As a
consequence, we can obtain a factor- approximation algorithm by
setting and a factor- algorithm by
setting . Besides, by setting , an
approximation algorithm with ratio , i.e. an algorithm with
only a single factor ratio on cost, can be immediately obtained. To
the best of our knowledge, this is the first non-trivial approximation
algorithm for the BCP problem that strictly obeys the delay constraint.Comment: 12 page
Efficient Wireless Security Through Jamming, Coding and Routing
There is a rich recent literature on how to assist secure communication
between a single transmitter and receiver at the physical layer of wireless
networks through techniques such as cooperative jamming. In this paper, we
consider how these single-hop physical layer security techniques can be
extended to multi-hop wireless networks and show how to augment physical layer
security techniques with higher layer network mechanisms such as coding and
routing. Specifically, we consider the secure minimum energy routing problem,
in which the objective is to compute a minimum energy path between two network
nodes subject to constraints on the end-to-end communication secrecy and
goodput over the path. This problem is formulated as a constrained optimization
of transmission power and link selection, which is proved to be NP-hard.
Nevertheless, we show that efficient algorithms exist to compute both exact and
approximate solutions for the problem. In particular, we develop an exact
solution of pseudo-polynomial complexity, as well as an epsilon-optimal
approximation of polynomial complexity. Simulation results are also provided to
show the utility of our algorithms and quantify their energy savings compared
to a combination of (standard) security-agnostic minimum energy routing and
physical layer security. In the simulated scenarios, we observe that, by
jointly optimizing link selection at the network layer and cooperative jamming
at the physical layer, our algorithms reduce the network energy consumption by
half
The Network Improvement Problem for Equilibrium Routing
In routing games, agents pick their routes through a network to minimize
their own delay. A primary concern for the network designer in routing games is
the average agent delay at equilibrium. A number of methods to control this
average delay have received substantial attention, including network tolls,
Stackelberg routing, and edge removal.
A related approach with arguably greater practical relevance is that of
making investments in improvements to the edges of the network, so that, for a
given investment budget, the average delay at equilibrium in the improved
network is minimized. This problem has received considerable attention in the
literature on transportation research and a number of different algorithms have
been studied. To our knowledge, none of this work gives guarantees on the
output quality of any polynomial-time algorithm. We study a model for this
problem introduced in transportation research literature, and present both
hardness results and algorithms that obtain nearly optimal performance
guarantees.
- We first show that a simple algorithm obtains good approximation guarantees
for the problem. Despite its simplicity, we show that for affine delays the
approximation ratio of 4/3 obtained by the algorithm cannot be improved.
- To obtain better results, we then consider restricted topologies. For
graphs consisting of parallel paths with affine delay functions we give an
optimal algorithm. However, for graphs that consist of a series of parallel
links, we show the problem is weakly NP-hard.
- Finally, we consider the problem in series-parallel graphs, and give an
FPTAS for this case.
Our work thus formalizes the intuition held by transportation researchers
that the network improvement problem is hard, and presents topology-dependent
algorithms that have provably tight approximation guarantees.Comment: 27 pages (including abstract), 3 figure
A Survey on Delay-Aware Resource Control for Wireless Systems --- Large Deviation Theory, Stochastic Lyapunov Drift and Distributed Stochastic Learning
In this tutorial paper, a comprehensive survey is given on several major
systematic approaches in dealing with delay-aware control problems, namely the
equivalent rate constraint approach, the Lyapunov stability drift approach and
the approximate Markov Decision Process (MDP) approach using stochastic
learning. These approaches essentially embrace most of the existing literature
regarding delay-aware resource control in wireless systems. They have their
relative pros and cons in terms of performance, complexity and implementation
issues. For each of the approaches, the problem setup, the general solution and
the design methodology are discussed. Applications of these approaches to
delay-aware resource allocation are illustrated with examples in single-hop
wireless networks. Furthermore, recent results regarding delay-aware multi-hop
routing designs in general multi-hop networks are elaborated. Finally, the
delay performance of the various approaches are compared through simulations
using an example of the uplink OFDMA systems.Comment: 58 pages, 8 figures; IEEE Transactions on Information Theory, 201
Algorithmic Aspects of Energy-Delay Tradeoff in Multihop Cooperative Wireless Networks
We consider the problem of energy-efficient transmission in delay constrained
cooperative multihop wireless networks. The combinatorial nature of cooperative
multihop schemes makes it difficult to design efficient polynomial-time
algorithms for deciding which nodes should take part in cooperation, and when
and with what power they should transmit. In this work, we tackle this problem
in memoryless networks with or without delay constraints, i.e., quality of
service guarantee. We analyze a wide class of setups, including unicast,
multicast, and broadcast, and two main cooperative approaches, namely: energy
accumulation (EA) and mutual information accumulation (MIA). We provide a
generalized algorithmic formulation of the problem that encompasses all those
cases. We investigate the similarities and differences of EA and MIA in our
generalized formulation. We prove that the broadcast and multicast problems
are, in general, not only NP hard but also o(log(n)) inapproximable. We break
these problems into three parts: ordering, scheduling and power control, and
propose a novel algorithm that, given an ordering, can optimally solve the
joint power allocation and scheduling problems simultaneously in polynomial
time. We further show empirically that this algorithm used in conjunction with
an ordering derived heuristically using the Dijkstra's shortest path algorithm
yields near-optimal performance in typical settings. For the unicast case, we
prove that although the problem remains NP hard with MIA, it can be solved
optimally and in polynomial time when EA is used. We further use our algorithm
to study numerically the trade-off between delay and power-efficiency in
cooperative broadcast and compare the performance of EA vs MIA as well as the
performance of our cooperative algorithm with a smart noncooperative algorithm
in a broadcast setting.Comment: 12 pages, 9 figure
Survivability in Time-varying Networks
Time-varying graphs are a useful model for networks with dynamic connectivity
such as vehicular networks, yet, despite their great modeling power, many
important features of time-varying graphs are still poorly understood. In this
paper, we study the survivability properties of time-varying networks against
unpredictable interruptions. We first show that the traditional definition of
survivability is not effective in time-varying networks, and propose a new
survivability framework. To evaluate the survivability of time-varying networks
under the new framework, we propose two metrics that are analogous to MaxFlow
and MinCut in static networks. We show that some fundamental
survivability-related results such as Menger's Theorem only conditionally hold
in time-varying networks. Then we analyze the complexity of computing the
proposed metrics and develop several approximation algorithms. Finally, we
conduct trace-driven simulations to demonstrate the application of our
survivability framework to the robust design of a real-world bus communication
network
Distributed Approximation Algorithms for Weighted Shortest Paths
A distributed network is modeled by a graph having nodes (processors) and
diameter . We study the time complexity of approximating {\em weighted}
(undirected) shortest paths on distributed networks with a {\em
bandwidth restriction} on edges (the standard synchronous \congest model). The
question whether approximation algorithms help speed up the shortest paths
(more precisely distance computation) was raised since at least 2004 by Elkin
(SIGACT News 2004). The unweighted case of this problem is well-understood
while its weighted counterpart is fundamental problem in the area of
distributed approximation algorithms and remains widely open. We present new
algorithms for computing both single-source shortest paths (\sssp) and
all-pairs shortest paths (\apsp) in the weighted case.
Our main result is an algorithm for \sssp. Previous results are the classic
-time Bellman-Ford algorithm and an -time
-approximation algorithm, for any integer
, which follows from the result of Lenzen and Patt-Shamir (STOC 2013).
(Note that Lenzen and Patt-Shamir in fact solve a harder problem, and we use
to hide the O(\poly\log n) term.) We present an -time -approximation algorithm for \sssp. This
algorithm is {\em sublinear-time} as long as is sublinear, thus yielding a
sublinear-time algorithm with almost optimal solution. When is small, our
running time matches the lower bound of by Das Sarma
et al. (SICOMP 2012), which holds even when , up to a
\poly\log n factor.Comment: Full version of STOC 201
Networked Computing in Wireless Sensor Networks for Structural Health Monitoring
This paper studies the problem of distributed computation over a network of
wireless sensors. While this problem applies to many emerging applications, to
keep our discussion concrete we will focus on sensor networks used for
structural health monitoring. Within this context, the heaviest computation is
to determine the singular value decomposition (SVD) to extract mode shapes
(eigenvectors) of a structure. Compared to collecting raw vibration data and
performing SVD at a central location, computing SVD within the network can
result in significantly lower energy consumption and delay. Using recent
results on decomposing SVD, a well-known centralized operation, into
components, we seek to determine a near-optimal communication structure that
enables the distribution of this computation and the reassembly of the final
results, with the objective of minimizing energy consumption subject to a
computational delay constraint. We show that this reduces to a generalized
clustering problem; a cluster forms a unit on which a component of the overall
computation is performed. We establish that this problem is NP-hard. By
relaxing the delay constraint, we derive a lower bound to this problem. We then
propose an integer linear program (ILP) to solve the constrained problem
exactly as well as an approximate algorithm with a proven approximation ratio.
We further present a distributed version of the approximate algorithm. We
present both simulation and experimentation results to demonstrate the
effectiveness of these algorithms
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