168 research outputs found
An EPTAS for Scheduling on Unrelated Machines of Few Different Types
In the classical problem of scheduling on unrelated parallel machines, a set
of jobs has to be assigned to a set of machines. The jobs have a processing
time depending on the machine and the goal is to minimize the makespan, that is
the maximum machine load. It is well known that this problem is NP-hard and
does not allow polynomial time approximation algorithms with approximation
guarantees smaller than unless PNP. We consider the case that there
are only a constant number of machine types. Two machines have the same
type if all jobs have the same processing time for them. This variant of the
problem is strongly NP-hard already for . We present an efficient
polynomial time approximation scheme (EPTAS) for the problem, that is, for any
an assignment with makespan of length at most
times the optimum can be found in polynomial time in the
input length and the exponent is independent of . In particular
we achieve a running time of , where
denotes the input length. Furthermore, we study three other problem
variants and present an EPTAS for each of them: The Santa Claus problem, where
the minimum machine load has to be maximized; the case of scheduling on
unrelated parallel machines with a constant number of uniform types, where
machines of the same type behave like uniformly related machines; and the
multidimensional vector scheduling variant of the problem where both the
dimension and the number of machine types are constant. For the Santa Claus
problem we achieve the same running time. The results are achieved, using mixed
integer linear programming and rounding techniques
Precedence-constrained scheduling problems parameterized by partial order width
Negatively answering a question posed by Mnich and Wiese (Math. Program.
154(1-2):533-562), we show that P2|prec,|, the
problem of finding a non-preemptive minimum-makespan schedule for
precedence-constrained jobs of lengths 1 and 2 on two parallel identical
machines, is W[2]-hard parameterized by the width of the partial order giving
the precedence constraints. To this end, we show that Shuffle Product, the
problem of deciding whether a given word can be obtained by interleaving the
letters of other given words, is W[2]-hard parameterized by , thus
additionally answering a question posed by Rizzi and Vialette (CSR 2013).
Finally, refining a geometric algorithm due to Servakh (Diskretn. Anal. Issled.
Oper. 7(1):75-82), we show that the more general Resource-Constrained Project
Scheduling problem is fixed-parameter tractable parameterized by the partial
order width combined with the maximum allowed difference between the earliest
possible and factual starting time of a job.Comment: 14 pages plus appendi
A New Lower Bound for Deterministic Truthful Scheduling
We study the problem of truthfully scheduling tasks to selfish
unrelated machines, under the objective of makespan minimization, as was
introduced in the seminal work of Nisan and Ronen [STOC'99]. Closing the
current gap of on the approximation ratio of deterministic truthful
mechanisms is a notorious open problem in the field of algorithmic mechanism
design. We provide the first such improvement in more than a decade, since the
lower bounds of (for ) and (for ) by
Christodoulou et al. [SODA'07] and Koutsoupias and Vidali [MFCS'07],
respectively. More specifically, we show that the currently best lower bound of
can be achieved even for just machines; for we already get
the first improvement, namely ; and allowing the number of machines to
grow arbitrarily large we can get a lower bound of .Comment: 15 page
Star Routing: Between Vehicle Routing and Vertex Cover
We consider an optimization problem posed by an actual newspaper company,
which consists of computing a minimum length route for a delivery truck, such
that the driver only stops at street crossings, each time delivering copies to
all customers adjacent to the crossing. This can be modeled as an abstract
problem that takes an unweighted simple graph and a subset of
edges and asks for a shortest cycle, not necessarily simple, such that
every edge of has an endpoint in the cycle.
We show that the decision version of the problem is strongly NP-complete,
even if is a grid graph. Regarding approximate solutions, we show that the
general case of the problem is APX-hard, and thus no PTAS is possible unless P
NP. Despite the hardness of approximation, we show that given any
-approximation algorithm for metric TSP, we can build a
-approximation algorithm for our optimization problem, yielding a
concrete -approximation algorithm.
The grid case is of particular importance, because it models a city map or
some part of it. A usual scenario is having some neighborhood full of
customers, which translates as an instance of the abstract problem where almost
every edge of is in . We model this property as , and
for these instances we give a -approximation algorithm,
for any , provided that the grid is sufficiently big.Comment: Accepted to the 12th Annual International Conference on Combinatorial
Optimization and Applications (COCOA'18
An Optimization Approach to the Ordering Phase of an Attended Home Delivery Service
Attended Home Delivery (AHD) systems are used whenever a supplying company
offers online shopping services that require that customers must be present
when their deliveries arrive. Therefore, the supplying company and the customer
must both agree on a time window, which ideally is rather short, during which
delivery is guaranteed. Typically, a capacitated Vehicle Routing Problem with
Time Windows forms the underlying optimization problem of the AHD system. In
this work, we consider an AHD system that runs the online grocery shopping
service of an international grocery retailer. The ordering phase, during which
customers place their orders through the web service, is the computationally
most challenging part of the AHD system. The delivery schedule must be built
dynamically as new orders are placed. We propose a solution approach that
allows to (non-stochastically) determine which delivery time windows can be
offered to potential customers. We split the computations of the ordering phase
into four key steps. For performing these basic steps we suggest both a
heuristic approach and a hybrid approach employing mixed-integer linear
programs. In an experimental evaluation we demonstrate the efficiency of our
approaches
Genome sequencing of the extinct Eurasian wild aurochs, Bos primigenius, illuminates the phylogeography and evolution of cattle
Background
Domestication of the now-extinct wild aurochs, Bos primigenius, gave rise to the two major domestic extant cattle taxa, B. taurus and B. indicus. While previous genetic studies have shed some light on the evolutionary relationships between European aurochs and modern cattle, important questions remain unanswered, including the phylogenetic status of aurochs, whether gene flow from aurochs into early domestic populations occurred, and which genomic regions were subject to selection processes during and after domestication. Here, we address these questions using whole-genome sequencing data generated from an approximately 6,750-year-old British aurochs bone and genome sequence data from 81 additional cattle plus genome-wide single nucleotide polymorphism data from a diverse panel of 1,225 modern animals.
Results
Phylogenomic analyses place the aurochs as a distinct outgroup to the domestic B. taurus lineage, supporting the predominant Near Eastern origin of European cattle. Conversely, traditional British and Irish breeds share more genetic variants with this aurochs specimen than other European populations, supporting localized gene flow from aurochs into the ancestors of modern British and Irish cattle, perhaps through purposeful restocking by early herders in Britain. Finally, the functions of genes showing evidence for positive selection in B. taurus are enriched for neurobiology, growth, metabolism and immunobiology, suggesting that these biological processes have been important in the domestication of cattle.
Conclusions
This work provides important new information regarding the origins and functional evolution of modern cattle, revealing that the interface between early European domestic populations and wild aurochs was significantly more complex than previously thought
On the Origin of Indonesian Cattle
Background: Two bovine species contribute to the Indonesian livestock, zebu (Bos indicus) and banteng (Bos javanicus), respectively. Although male hybrid offspring of these species is not fertile, Indonesian cattle breeds are supposed to be of mixed species origin. However, this has not been documented and is so far only supported by preliminary molecular analysis. Methods and Findings: Analysis of mitochondrial, Y-chromosomal and microsatellite DNA showed a banteng introgression of 10-16% in Indonesian zebu breeds. East-Javanese Madura and Galekan cattle have higher levels of autosomal banteng introgression (20-30%) and combine a zebu paternal lineage with a predominant (Madura) or even complete (Galekan) maternal banteng origin. Two Madura bulls carried taurine Y-chromosomal haplotypes, presumably of French Limousin origin. In contrast, we did not find evidence for zebu introgression in five populations of the Bali cattle, a domestic form of the banteng. Conclusions: Because of their unique species composition Indonesian cattle represent a valuable genetic resource, which potentially may also be exploited in other tropical regions. Ā© 2009 Mohamad et al
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