27,943 research outputs found
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
On Generalizations of Network Design Problems with Degree Bounds
Iterative rounding and relaxation have arguably become the method of choice
in dealing with unconstrained and constrained network design problems. In this
paper we extend the scope of the iterative relaxation method in two directions:
(1) by handling more complex degree constraints in the minimum spanning tree
problem (namely, laminar crossing spanning tree), and (2) by incorporating
`degree bounds' in other combinatorial optimization problems such as matroid
intersection and lattice polyhedra. We give new or improved approximation
algorithms, hardness results, and integrality gaps for these problems.Comment: v2, 24 pages, 4 figure
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
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