25,224 research outputs found
Time and Location Aware Mobile Data Pricing
Mobile users' correlated mobility and data consumption patterns often lead to
severe cellular network congestion in peak hours and hot spots. This paper
presents an optimal design of time and location aware mobile data pricing,
which incentivizes users to smooth traffic and reduce network congestion. We
derive the optimal pricing scheme through analyzing a two-stage decision
process, where the operator determines the time and location aware prices by
minimizing his total cost in Stage I, and each mobile user schedules his mobile
traffic by maximizing his payoff (i.e., utility minus payment) in Stage II. We
formulate the two-stage decision problem as a bilevel optimization problem, and
propose a derivative-free algorithm to solve the problem for any increasing
concave user utility functions. We further develop low complexity algorithms
for the commonly used logarithmic and linear utility functions. The optimal
pricing scheme ensures a win-win situation for the operator and users.
Simulations show that the operator can reduce the cost by up to 97.52% in the
logarithmic utility case and 98.70% in the linear utility case, and users can
increase their payoff by up to 79.69% and 106.10% for the two types of
utilities, respectively, comparing with a time and location independent pricing
benchmark. Our study suggests that the operator should provide price discounts
at less crowded time slots and locations, and the discounts need to be
significant when the operator's cost of provisioning excessive traffic is high
or users' willingness to delay traffic is low.Comment: This manuscript serves as the online technical report of the article
accepted by IEEE Transactions on Mobile Computin
On-Line End-to-End Congestion Control
Congestion control in the current Internet is accomplished mainly by TCP/IP.
To understand the macroscopic network behavior that results from TCP/IP and
similar end-to-end protocols, one main analytic technique is to show that the
the protocol maximizes some global objective function of the network traffic.
Here we analyze a particular end-to-end, MIMD (multiplicative-increase,
multiplicative-decrease) protocol. We show that if all users of the network use
the protocol, and all connections last for at least logarithmically many
rounds, then the total weighted throughput (value of all packets received) is
near the maximum possible. Our analysis includes round-trip-times, and (in
contrast to most previous analyses) gives explicit convergence rates, allows
connections to start and stop, and allows capacities to change.Comment: Proceedings IEEE Symp. Foundations of Computer Science, 200
Fast and Deterministic Approximations for k-Cut
In an undirected graph, a k-cut is a set of edges whose removal breaks the graph into at least k connected components. The minimum weight k-cut can be computed in n^O(k) time, but when k is treated as part of the input, computing the minimum weight k-cut is NP-Hard [Goldschmidt and Hochbaum, 1994]. For poly(m,n,k)-time algorithms, the best possible approximation factor is essentially 2 under the small set expansion hypothesis [Manurangsi, 2017]. Saran and Vazirani [1995] showed that a (2 - 2/k)-approximately minimum weight k-cut can be computed via O(k) minimum cuts, which implies a O~(km) randomized running time via the nearly linear time randomized min-cut algorithm of Karger [2000]. Nagamochi and Kamidoi [2007] showed that a (2 - 2/k)-approximately minimum weight k-cut can be computed deterministically in O(mn + n^2 log n) time. These results prompt two basic questions. The first concerns the role of randomization. Is there a deterministic algorithm for 2-approximate k-cuts matching the randomized running time of O~(km)? The second question qualitatively compares minimum cut to 2-approximate minimum k-cut. Can 2-approximate k-cuts be computed as fast as the minimum cut - in O~(m) randomized time?
We give a deterministic approximation algorithm that computes (2 + eps)-minimum k-cuts in O(m log^3 n / eps^2) time, via a (1 + eps)-approximation for an LP relaxation of k-cut
Approximating the Held-Karp Bound for Metric TSP in Nearly Linear Time
We give a nearly linear time randomized approximation scheme for the
Held-Karp bound [Held and Karp, 1970] for metric TSP. Formally, given an
undirected edge-weighted graph on edges and , the
algorithm outputs in time, with high probability, a
-approximation to the Held-Karp bound on the metric TSP instance
induced by the shortest path metric on . The algorithm can also be used to
output a corresponding solution to the Subtour Elimination LP. We substantially
improve upon the running time achieved previously
by Garg and Khandekar. The LP solution can be used to obtain a fast randomized
-approximation for metric TSP which improves
upon the running time of previous implementations of Christofides' algorithm
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