16,786 research outputs found
Minimum Entropy Orientations
We study graph orientations that minimize the entropy of the in-degree
sequence. The problem of finding such an orientation is an interesting special
case of the minimum entropy set cover problem previously studied by Halperin
and Karp [Theoret. Comput. Sci., 2005] and by the current authors
[Algorithmica, to appear]. We prove that the minimum entropy orientation
problem is NP-hard even if the graph is planar, and that there exists a simple
linear-time algorithm that returns an approximate solution with an additive
error guarantee of 1 bit. This improves on the only previously known algorithm
which has an additive error guarantee of log_2 e bits (approx. 1.4427 bits).Comment: Referees' comments incorporate
Sensor placement for fault location identification in water networks: A minimum test cover approach
This paper focuses on the optimal sensor placement problem for the
identification of pipe failure locations in large-scale urban water systems.
The problem involves selecting the minimum number of sensors such that every
pipe failure can be uniquely localized. This problem can be viewed as a minimum
test cover (MTC) problem, which is NP-hard. We consider two approaches to
obtain approximate solutions to this problem. In the first approach, we
transform the MTC problem to a minimum set cover (MSC) problem and use the
greedy algorithm that exploits the submodularity property of the MSC problem to
compute the solution to the MTC problem. In the second approach, we develop a
new \textit{augmented greedy} algorithm for solving the MTC problem. This
approach does not require the transformation of the MTC to MSC. Our augmented
greedy algorithm provides in a significant computational improvement while
guaranteeing the same approximation ratio as the first approach. We propose
several metrics to evaluate the performance of the sensor placement designs.
Finally, we present detailed computational experiments for a number of real
water distribution networks
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