364 research outputs found
Single-source k-splittable min-cost flows
Motivated by a famous open question on the single-source unsplittable minimum cost flow problem, we present a new approximation result for the relaxation of the problem where, for a given number k, each commodity must be routed along at most k paths
WiLiTV: A Low-Cost Wireless Framework for Live TV Services
With the evolution of HDTV and Ultra HDTV, the bandwidth requirement for
IP-based TV content is rapidly increasing. Consumers demand uninterrupted
service with a high Quality of Experience (QoE). Service providers are
constantly trying to differentiate themselves by innovating new ways of
distributing content more efficiently with lower cost and higher penetration.
In this work, we propose a cost-efficient wireless framework (WiLiTV) for
delivering live TV services, consisting of a mix of wireless access
technologies (e.g. Satellite, WiFi and LTE overlay links). In the proposed
architecture, live TV content is injected into the network at a few residential
locations using satellite dishes. The content is then further distributed to
other homes using a house-to-house WiFi network or via an overlay LTE network.
Our problem is to construct an optimal TV distribution network with the minimum
number of satellite injection points, while preserving the highest QoE, for
different neighborhood densities. We evaluate the framework using realistic
time-varying demand patterns and a diverse set of home location data. Our study
demonstrates that the architecture requires 75 - 90% fewer satellite injection
points, compared to traditional architectures. Furthermore, we show that most
cost savings can be obtained using simple and practical relay routing
solutions
Optimizing Emergency Transportation through Multicommodity Quickest Paths
In transportation networks with limited capacities and travel times on the arcs, a class of problems attracting a growing scientific interest is represented by the optimal routing and scheduling of given amounts of flow to be transshipped from the origin points to the specific destinations in minimum time. Such problems are of particular concern to emergency transportation where evacuation plans seek to minimize the time evacuees need to clear the affected area and reach the safe zones. Flows over time approaches are among the most suitable mathematical tools to provide a modelling representation of these problems from a macroscopic point of view. Among them, the Quickest Path Problem (QPP), requires an origin-destination flow to be routed on a single path while taking into account inflow limits on the arcs and minimizing the makespan, namely, the time instant when the last unit of flow reaches its destination. In the context of emergency transport, the QPP represents a relevant modelling tool, since its solutions are based on unsplittable dynamic flows that can support the development of evacuation plans which are very easy to be correctly implemented, assigning one single evacuation path to a whole population. This way it is possible to prevent interferences, turbulence, and congestions that may affect the transportation process, worsening the overall clearing time. Nevertheless, the current state-of-the-art presents a lack of studies on multicommodity generalizations of the QPP, where network flows refer to various populations, possibly with different origins and destinations. In this paper we provide a contribution to fill this gap, by considering the Multicommodity Quickest Path Problem (MCQPP), where multiple commodities, each with its own origin, destination and demand, must be routed on a capacitated network with travel times on the arcs, while minimizing the overall makespan and allowing the flow associated to each commodity to be routed on a single path. For this optimization problem, we provide the first mathematical formulation in the scientific literature, based on mixed integer programming and encompassing specific features aimed at empowering the suitability of the arising solutions in real emergency transportation plans. A computational experience performed on a set of benchmark instances is then presented to provide a proof-of-concept for our original model and to evaluate the quality and suitability of the provided solutions together with the required computational effort. Most of the instances are solved at the optimum by a commercial MIP solver, fed with a lower bound deriving from the optimal makespan of a splittable-flow relaxation of the MCQPP
Energy management in communication networks: a journey through modelling and optimization glasses
The widespread proliferation of Internet and wireless applications has
produced a significant increase of ICT energy footprint. As a response, in the
last five years, significant efforts have been undertaken to include
energy-awareness into network management. Several green networking frameworks
have been proposed by carefully managing the network routing and the power
state of network devices.
Even though approaches proposed differ based on network technologies and
sleep modes of nodes and interfaces, they all aim at tailoring the active
network resources to the varying traffic needs in order to minimize energy
consumption. From a modeling point of view, this has several commonalities with
classical network design and routing problems, even if with different
objectives and in a dynamic context.
With most researchers focused on addressing the complex and crucial
technological aspects of green networking schemes, there has been so far little
attention on understanding the modeling similarities and differences of
proposed solutions. This paper fills the gap surveying the literature with
optimization modeling glasses, following a tutorial approach that guides
through the different components of the models with a unified symbolism. A
detailed classification of the previous work based on the modeling issues
included is also proposed
Cluster Before You Hallucinate: Approximating Node-Capacitated Network Design and Energy Efficient Routing
We consider circuit routing with an objective of minimizing energy, in a
network of routers that are speed scalable and that may be shutdown when idle.
We consider both multicast routing and unicast routing. It is known that this
energy minimization problem can be reduced to a capacitated flow network design
problem, where vertices have a common capacity but arbitrary costs, and the
goal is to choose a minimum cost collection of vertices whose induced subgraph
will support the specified flow requirements. For the multicast (single-sink)
capacitated design problem we give a polynomial-time algorithm that is
O(log^3n)-approximate with O(log^4 n) congestion. This translates back to a
O(log ^(4{\alpha}+3) n)-approximation for the multicast energy-minimization
routing problem, where {\alpha} is the polynomial exponent in the dynamic power
used by a router. For the unicast (multicommodity) capacitated design problem
we give a polynomial-time algorithm that is O(log^5 n)-approximate with
O(log^12 n) congestion, which translates back to a O(log^(12{\alpha}+5)
n)-approximation for the unicast energy-minimization routing problem.Comment: 22 pages (full version of STOC 2014 paper
Strong Nash Equilibria in Games with the Lexicographical Improvement Property
We introduce a class of finite strategic games with the property that every
deviation of a coalition of players that is profitable to each of its members
strictly decreases the lexicographical order of a certain function defined on
the set of strategy profiles. We call this property the Lexicographical
Improvement Property (LIP) and show that it implies the existence of a
generalized strong ordinal potential function. We use this characterization to
derive existence, efficiency and fairness properties of strong Nash equilibria.
We then study a class of games that generalizes congestion games with
bottleneck objectives that we call bottleneck congestion games. We show that
these games possess the LIP and thus the above mentioned properties. For
bottleneck congestion games in networks, we identify cases in which the
potential function associated with the LIP leads to polynomial time algorithms
computing a strong Nash equilibrium. Finally, we investigate the LIP for
infinite games. We show that the LIP does not imply the existence of a
generalized strong ordinal potential, thus, the existence of SNE does not
follow. Assuming that the function associated with the LIP is continuous,
however, we prove existence of SNE. As a consequence, we prove that bottleneck
congestion games with infinite strategy spaces and continuous cost functions
possess a strong Nash equilibrium
Flow Maximization Problem as Linear Programming Problem with Capacity Constraints
Flow maximization is a fundamental problem in mathematics; there are several algorithms available to solve this problem, but these algorithms have some limitations. This paper presents the flow maximization problem as a Linear Programming Problem (L.P.P.). The solution given by L.P.P. formulation of the problem and provided by Ford Fulkerson algorithm is same. This paper also compares the single path flow and k-splitting of the flow and suggests that k-splitting of flow is better than single path flow
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