357 research outputs found
Capacitated Vehicle Routing with Non-Uniform Speeds
The capacitated vehicle routing problem (CVRP) involves distributing
(identical) items from a depot to a set of demand locations, using a single
capacitated vehicle. We study a generalization of this problem to the setting
of multiple vehicles having non-uniform speeds (that we call Heterogenous
CVRP), and present a constant-factor approximation algorithm.
The technical heart of our result lies in achieving a constant approximation
to the following TSP variant (called Heterogenous TSP). Given a metric denoting
distances between vertices, a depot r containing k vehicles with possibly
different speeds, the goal is to find a tour for each vehicle (starting and
ending at r), so that every vertex is covered in some tour and the maximum
completion time is minimized. This problem is precisely Heterogenous CVRP when
vehicles are uncapacitated.
The presence of non-uniform speeds introduces difficulties for employing
standard tour-splitting techniques. In order to get a better understanding of
this technique in our context, we appeal to ideas from the 2-approximation for
scheduling in parallel machine of Lenstra et al.. This motivates the
introduction of a new approximate MST construction called Level-Prim, which is
related to Light Approximate Shortest-path Trees. The last component of our
algorithm involves partitioning the Level-Prim tree and matching the resulting
parts to vehicles. This decomposition is more subtle than usual since now we
need to enforce correlation between the size of the parts and their distances
to the depot
Locating Depots for Capacitated Vehicle Routing
We study a location-routing problem in the context of capacitated vehicle
routing. The input is a set of demand locations in a metric space and a fleet
of k vehicles each of capacity Q. The objective is to locate k depots, one for
each vehicle, and compute routes for the vehicles so that all demands are
satisfied and the total cost is minimized. Our main result is a constant-factor
approximation algorithm for this problem. To achieve this result, we reduce to
the k-median-forest problem, which generalizes both k-median and minimum
spanning tree, and which might be of independent interest. We give a
(3+c)-approximation algorithm for k-median-forest, which leads to a
(12+c)-approximation algorithm for the above location-routing problem, for any
constant c>0. The algorithm for k-median-forest is just t-swap local search,
and we prove that it has locality gap 3+2/t; this generalizes the corresponding
result known for k-median. Finally we consider the "non-uniform"
k-median-forest problem which has different cost functions for the MST and
k-median parts. We show that the locality gap for this problem is unbounded
even under multi-swaps, which contrasts with the uniform case. Nevertheless, we
obtain a constant-factor approximation algorithm, using an LP based approach.Comment: 12 pages, 1 figur
Approximating k-Forest with Resource Augmentation: A Primal-Dual Approach
In this paper, we study the -forest problem in the model of resource
augmentation. In the -forest problem, given an edge-weighted graph ,
a parameter , and a set of demand pairs , the
objective is to construct a minimum-cost subgraph that connects at least
demands. The problem is hard to approximate---the best-known approximation
ratio is . Furthermore, -forest is as hard to
approximate as the notoriously-hard densest -subgraph problem.
While the -forest problem is hard to approximate in the worst-case, we
show that with the use of resource augmentation, we can efficiently approximate
it up to a constant factor.
First, we restate the problem in terms of the number of demands that are {\em
not} connected. In particular, the objective of the -forest problem can be
viewed as to remove at most demands and find a minimum-cost subgraph that
connects the remaining demands. We use this perspective of the problem to
explain the performance of our algorithm (in terms of the augmentation) in a
more intuitive way.
Specifically, we present a polynomial-time algorithm for the -forest
problem that, for every , removes at most demands and has
cost no more than times the cost of an optimal algorithm
that removes at most demands
Stochastic Vehicle Routing with Recourse
We study the classic Vehicle Routing Problem in the setting of stochastic
optimization with recourse. StochVRP is a two-stage optimization problem, where
demand is satisfied using two routes: fixed and recourse. The fixed route is
computed using only a demand distribution. Then after observing the demand
instantiations, a recourse route is computed -- but costs here become more
expensive by a factor lambda.
We present an O(log^2 n log(n lambda))-approximation algorithm for this
stochastic routing problem, under arbitrary distributions. The main idea in
this result is relating StochVRP to a special case of submodular orienteering,
called knapsack rank-function orienteering. We also give a better approximation
ratio for knapsack rank-function orienteering than what follows from prior
work. Finally, we provide a Unique Games Conjecture based omega(1) hardness of
approximation for StochVRP, even on star-like metrics on which our algorithm
achieves a logarithmic approximation.Comment: 20 Pages, 1 figure Revision corrects the statement and proof of
Theorem 1.
A novel model of common Toll-like receptor 4- and injury-induced transcriptional themes in human leukocytes
Configuraciones del poder punitivo a escala local. Juventudes y cuerpos marcados como femeninos en la historia reciente
En la presente reseña nos proponemos sintetizar los principales avances del proyecto de investigación “Configuraciones del poder punitivo a escala local. Juventudes y cuerpos marcados como femeninos en la historia reciente”. En un primer acercamiento analizamos las acciones y discursos de las agencias formales del sistema penal a partir de los números del “giro punitivo” (tasa de prisionalización, tipologías delictivas, pena, edad de los imputados, género y ocupación) y su relación con los nuevos dispositivos normativos del período estudiado (1990/2019); en la segunda parte exploramos como se expresa tal cambio del paradigma en las agencias informales del sistema. Especialmente, nos interesa explorar los lazos del tratamiento judicial de algunos casos vinculados a los cuerpos marcados como femeninos con los discursos mediáticos y callejeros que han habilitado dispositivos de control, vigilancia y hostigamiento. 
Del orden de las milicias al orden de las instituciones: agencias de control y nuevas disciplinas en Santa Fe y Entre Ríos entre 1860 y 1880
El presente artículo se propone reseñar los principales hallazgos del proyecto en el que investigamos las nuevas configuraciones del orden jurídico durante la segunda mitad del siglo XIX en el territorio santafesino y entrerriano, período durante el cual la región participó de un acelerado proceso de institucionalización de su estructura estatal en tanto progresaba la formación de un régimen moderno de dominación y su incorporación plena al sistema capitalista.Con el objeto de aproximarnos a aquel régimen de gobierno y modernización estatal que subyace en las formas institucionales y en las prácticas sociales de las nuevas agencias estatales, analizaremos comparativamente la instrumentación jurídica y práctica de aquellas agencias que capilarmente constituyen a los nuevos órdenes provinciales en Santa Fe y Entre Ríos entre 1860 y 1880, antes de la definitiva consolidación de la dominación en la forma moderna del estado nacional. Y en un apartado final, a modo de conclusión, reflexionaremos sobre la experiencia de investigación desde una perspectiva teórico-metodológica
Multiple target three-dimensional coordinate estimation for bistatic MIMO radar with uniform linear receive array
Controlled mobility in stochastic and dynamic wireless networks
We consider the use of controlled mobility in wireless networks where messages arriving randomly in time and space are collected by mobile receivers (collectors). The collectors are responsible for receiving these messages via wireless transmission by dynamically adjusting their position in the network. Our goal is to utilize a combination of wireless transmission and controlled mobility to improve the throughput and delay performance in such networks. First, we consider a system with a single collector. We show that the necessary and sufficient stability condition for such a system is given by ρ<1 where ρ is the expected system load. We derive lower bounds for the expected message waiting time in the system and develop policies that are stable for all loads ρ<1 and have asymptotically optimal delay scaling. We show that the combination of mobility and wireless transmission results in a delay scaling of Θ([1 over 1−ρ]) with the system load ρ, in contrast to the Θ([1 over (1−ρ)[superscript 2]]) delay scaling in the corresponding system without wireless transmission, where the collector visits each message location. Next, we consider the system with multiple collectors. In the case where simultaneous transmissions to different collectors do not interfere with each other, we show that both the stability condition and the delay scaling extend from the single collector case. In the case where simultaneous transmissions to different collectors interfere with each other, we characterize the stability region of the system and show that a frame-based version of the well-known Max-Weight policy stabilizes the system asymptotically in the frame length.National Science Foundation (U.S.) (Grant CNS-0915988)United States. Army Research Office. Multidisciplinary University Research Initiative (Grant W911NF-08-1-0238
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