52,215 research outputs found
Towards a taxonomy of parallel branch and bound algorithms
In this paper we present a classification of parallel branch and bound algorithms, and
elaborate on the consequences of particular parameter settings. The taxonomy is based upon
how the algorithms handle the knowledge about the problem instance to be solved, generated
during execution. The starting point of the taxonomy is the generally accepted description
of the sequential branch and bound algorithm, as presented in, for example, [Mitten 1970]
and [Ibaraki 1976a, 1976b, 1977a, 1977b]
Towards an abstract parallel branch and bound machine
Many (parallel) branch and bound algorithms look very different from each other at first
glance. They exploit, however, the same underlying computational model. This phenomenon
can be used to define branch and bound algorithms in terms of a set of basic rules that are applied in a specific (predefined) order.
In the sequential case, the specification of Mitten's rules turns out to be sufficient for
the development of branch and bound algorithms. In the parallel case, the situation is a
bit more complicated. We have to consider extra parameters such as work distribution and
knowledge sharing. Here, the implementation of parallel branch and bound algorithms can be
seen as a tuning of the parameters combined with the specification of Mitten's rules.
These observations lead to generic systems, where the user provides the specifications of
the problem to be solved, and the system generates a branch and bound algorithm running on
a specific architecture. We will discuss some proposals that appeared in the literature.
Next, we raise the question whether the proposed models are flexible enough. We analyze
the design decisions to be taken when implementing a parallel branch and bound algorithm.
It results in a classification model, which is validated by checking whether it captures
existing branch and bound implementations.
Finally, we return to the issue of flexibility of existing systems, and propose to add an
abstract machine model to the generic framework. The model defines a virtual parallel
branch and bound machine, within which the design decisions can be expressed in terms of
the abstract machine. We will outline some ideas on which the machine may be based, and
present directions of future work
Parallel branch and bound on an MIMD system
In this paper we give a classification of parallel branch and bound algorithms and
develop a class of asynchronous branch and bound algorithms for execution on an MIMD system.
We develop sufficient conditions to prevent the anomalies that can occur due to the
parallelism, the asynchronicity or the nondeter- minism, from degrading the performance of
the algorithm. Such conditions were known already for the synchronous case. It turns out that these conditions are sufficient for asynchronous algorithms as well. We also investigate the consequences of nonhomogeneous processing elements in a parallel computer system.
We introduce the notions of perfect parallel time and achieved efficiency to empirically
measure the effects of parallelism, because the traditional notions of speedup and efficiency are not capable of fully characterizing the actual execution of an asyn-chronous parallel algorithm.
Finally we present some computational results obtained for the symmetric traveling
salesman problem
Cross-Lingual Adaptation using Structural Correspondence Learning
Cross-lingual adaptation, a special case of domain adaptation, refers to the
transfer of classification knowledge between two languages. In this article we
describe an extension of Structural Correspondence Learning (SCL), a recently
proposed algorithm for domain adaptation, for cross-lingual adaptation. The
proposed method uses unlabeled documents from both languages, along with a word
translation oracle, to induce cross-lingual feature correspondences. From these
correspondences a cross-lingual representation is created that enables the
transfer of classification knowledge from the source to the target language.
The main advantages of this approach over other approaches are its resource
efficiency and task specificity.
We conduct experiments in the area of cross-language topic and sentiment
classification involving English as source language and German, French, and
Japanese as target languages. The results show a significant improvement of the
proposed method over a machine translation baseline, reducing the relative
error due to cross-lingual adaptation by an average of 30% (topic
classification) and 59% (sentiment classification). We further report on
empirical analyses that reveal insights into the use of unlabeled data, the
sensitivity with respect to important hyperparameters, and the nature of the
induced cross-lingual correspondences
Fine-grained Search Space Classification for Hard Enumeration Variants of Subset Problems
We propose a simple, powerful, and flexible machine learning framework for
(i) reducing the search space of computationally difficult enumeration variants
of subset problems and (ii) augmenting existing state-of-the-art solvers with
informative cues arising from the input distribution. We instantiate our
framework for the problem of listing all maximum cliques in a graph, a central
problem in network analysis, data mining, and computational biology. We
demonstrate the practicality of our approach on real-world networks with
millions of vertices and edges by not only retaining all optimal solutions, but
also aggressively pruning the input instance size resulting in several fold
speedups of state-of-the-art algorithms. Finally, we explore the limits of
scalability and robustness of our proposed framework, suggesting that
supervised learning is viable for tackling NP-hard problems in practice.Comment: AAAI 201
Solving Lotsizing Problems on Parallel Identical Machines Using Symmetry Breaking Constraints
Production planning on multiple parallel machines is an interesting problem, both from a theoretical and practical point of view. The parallel machine lotsizing problem consists of finding the optimal timing and level of production and the best allocation of products to machines. In this paper we look at how to incorporate parallel machines in a Mixed Integer Programming model when using commercial optimization software. More specifically, we look at the issue of symmetry. When multiple identical machines are available, many alternative optimal solutions can be created by renumbering the machines. These alternative solutions lead to difficulties in the branch-and-bound algorithm. We propose new constraints to break this symmetry. We tested our approach on the parallel machine lotsizing problem with setup costs and times, using a network reformulation for this problem. Computational tests indicate that several of the proposed symmetry breaking constraints substantially improve the solution time, except when used for solving the very easy problems. The results highlight the importance of creative modeling in solving Mixed Integer Programming problems.Mixed Integer Programming;Formulations;Symmetry;Lotsizing
Parallel String Sample Sort
We discuss how string sorting algorithms can be parallelized on modern
multi-core shared memory machines. As a synthesis of the best sequential string
sorting algorithms and successful parallel sorting algorithms for atomic
objects, we propose string sample sort. The algorithm makes effective use of
the memory hierarchy, uses additional word level parallelism, and largely
avoids branch mispredictions. Additionally, we parallelize variants of multikey
quicksort and radix sort that are also useful in certain situations.Comment: 34 pages, 7 figures and 12 table
Multi-Channel Scheduling for Fast Convergecast in Wireless Sensor Networks
We explore the following fundamental question -
how fast can information be collected from a wireless sensor
network? We consider a number of design parameters such
as, power control, time and frequency scheduling, and routing.
There are essentially two factors that hinder efficient data
collection - interference and the half-duplex single-transceiver
radios. We show that while power control helps in reducing the
number of transmission slots to complete a convergecast under a
single frequency channel, scheduling transmissions on different
frequency channels is more efficient in mitigating the effects of
interference (empirically, 6 channels suffice for most 100-node
networks). With these observations, we define a receiver-based
channel assignment problem, and prove it to be NP-complete on
general graphs. We then introduce a greedy channel assignment
algorithm that efficiently eliminates interference, and compare
its performance with other existing schemes via simulations.
Once the interference is completely eliminated, we show that
with half-duplex single-transceiver radios the achievable schedule
length is lower-bounded by max(2nk − 1,N), where nk is the
maximum number of nodes on any subtree and N is the number
of nodes in the network. We modify an existing distributed time
slot assignment algorithm to achieve this bound when a suitable
balanced routing scheme is employed. Through extensive simulations,
we demonstrate that convergecast can be completed within
up to 50% less time slots, in 100-node networks, using multiple
channels as compared to that with single-channel communication.
Finally, we also demonstrate further improvements that are
possible when the sink is equipped with multiple transceivers
or when there are multiple sinks to collect data
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