This work presents a classification of weak models of distributed computing. We focus on deterministic distributed algorithms, and study models of computing that are weaker versions of the widely-studied port-numbering model. In the port-numbering model, a node of degree @math d receives messages through @math d input ports and sends messages through @math d output ports, both numbered with @math 1 , 2 , ? , d . In this work, @math VV c is the class of all graph problems that can be solved in the standard port-numbering model. We study the following subclasses of @math VV c : Now we have many trivial containment relations, such as @math SB ⊆ MB ⊆ VB ⊆ VV ⊆ VV c , but it is not obvious if, for example, either of @math VB ⊆ SV or @math SV ⊆ VB should hold. Nevertheless, it turns out that we can identify a linear order on these classes. We prove that @math SB ? MB = VB ? SV = MV = VV ? VV c . The same holds for the constant-time versions of these classes. We also show that the constant-time variants of these classes can be characterised by a corresponding modal logic. Hence the linear order identified in this work has direct implications in the study of the expressibility of modal logic. Conversely, one can use tools from modal logic to study these classes.
The study of the port-numbering model was initiated by Angluin @cite_28 in 1980. Initially the main focus was on problems that have a nature---problems in which the local output of a node necessarily depends on the global properties of the input. Examples of papers from the first two decades after Angluin's pioneering work include @cite_31 , Yamashita and Kameda @cite_45 @cite_36 @cite_54 , and Boldi and Vigna @cite_7 , who studied global functions, leader election problems, spanning trees, and topological properties.
@cite_7 @cite_28 @cite_36 @cite_54 @cite_45 @cite_31
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This work presents a classification of weak models of distributed computing. We focus on deterministic distributed algorithms, and study models of computing that are weaker versions of the widely-studied port-numbering model. In the port-numbering model, a node of degree @math d receives messages through @math d input ports and sends messages through @math d output ports, both numbered with @math 1 , 2 , ? , d . In this work, @math VV c is the class of all graph problems that can be solved in the standard port-numbering model. We study the following subclasses of @math VV c : Now we have many trivial containment relations, such as @math SB ⊆ MB ⊆ VB ⊆ VV ⊆ VV c , but it is not obvious if, for example, either of @math VB ⊆ SV or @math SV ⊆ VB should hold. Nevertheless, it turns out that we can identify a linear order on these classes. We prove that @math SB ? MB = VB ? SV = MV = VV ? VV c . The same holds for the constant-time versions of these classes. We also show that the constant-time variants of these classes can be characterised by a corresponding modal logic. Hence the linear order identified in this work has direct implications in the study of the expressibility of modal logic. Conversely, one can use tools from modal logic to study these classes. This thesis describes a novel statistical named-entity (i.e. “proper name”) recognition system known as “MENE” (Maximum Entropy Named Entity). Named entity (N.E.) recognition is a form of information extraction in which we seek to classify every word in a document as being a person-name, organization, location, date, time, monetary value, percentage, or “none of the above”. The task has particular significance for Internet search engines, machine translation, the automatic indexing of documents, and as a foundation for work on more complex information extraction tasks. Two of the most significant problems facing the constructor of a named entity system are the questions of portability and system performance. A practical N.E. system will need to be ported frequently to new bodies of text and even to new languages. The challenge is to build a system which can be ported with minimal expense (in particular minimal programming by a computational linguist) while maintaining a high degree of accuracy in the new domains or languages. MENE attempts to address these issues through the use of maximum entropy probabilistic modeling. It utilizes a very flexible object-based architecture which allows it to make use of a broad range of knowledge sources in making its tagging decisions. In the DARPA-sponsored MUC-7 named entity evaluation, the system displayed an accuracy rate which was well-above the median, demonstrating that it can achieve the performance goal. In addition, we demonstrate that the system can be used as a post-processing tool to enhance the output of a hand-coded named entity recognizer through experiments in which MENE improved on the performance of N.E. systems from three different sites. Furthermore, when all three external recognizers are combined under MENE, we are able to achieve very strong results which, in some cases, appear to be competitive with human performance. Finally, we demonstrate the trans-lingual portability of the system. We ported the system to two Japanese-language named entity tasks, one of which involved a new named entity category, “artifact”. Our results on these tasks were competitive with the best systems built by native Japanese speakers despite the fact that the author speaks no Japanese. In the 0-extension problem, we are given a weighted graph with some nodes marked as terminals and a semimetric on the set of terminals. Our goal is to assign the rest of the nodes to terminals so as to minimize the sum, over all edges, of the product of the edge's weight and the distance between the terminals to which its endpoints are assigned. This problem generalizes the multiway cut problem of [SIAM J. Comput. , 23 (1994), pp. 864--894] and is closely related to the metric labeling problem introduced by Kleinberg and Tardos [Proceedings of the 40th IEEE Annual Symposium on Foundations of Computer Science, New York, 1999, pp. 14--23]. We present approximation algorithms for 0-Extension . In arbitrary graphs, we present a O(log k)-approximation algorithm, k being the number of terminals. We also give O(1)-approximation guarantees for weighted planar graphs. Our results are based on a natural metric relaxation of the problem previously considered by Karzanov [European J. Combin., 19 (1998), pp. 71--101]. It is similar in flavor to the linear programming relaxation of Garg, Vazirani, and Yannakakis [SIAM J. Comput. , 25 (1996), pp. 235--251] for the multicut problem, and similar to relaxations for other graph partitioning problems. We prove that the integrality ratio of the metric relaxation is at least @math for a positive c for infinitely many k. Our results improve some of the results of Kleinberg and Tardos, and they further our understanding on how to use metric relaxations. This paper studies the problem of constructing a minimum-weight spanning tree (MST) in a distributed network. This is one of the most important problems in the area of distributed computing. There is a long line of gradually improving protocols for this problem, and the state of the art today is a protocol with running time O(Λ(G)+n⋅log∗n) due to Kutten and Peleg [S. Kutten, D. Peleg, Fast distributed construction of k-dominating sets and applications, J. Algorithms 28 (1998) 40–66; preliminary version appeared in: Proc. of 14th ACM Symp. on Principles of Distributed Computing, Ottawa, Canada, August 1995, pp. 20–27], where Λ(G) denotes the diameter of the graph G. Peleg and Rubinovich [D. Peleg, V. Rubinovich, A near-tight lower bound on the time complexity of distributed MST construction, in: Proc. 40th IEEE Symp. on Foundations of Computer Science, 1999, pp. 253–261] have shown that Ω˜(n) time is required for constructing MST even on graphs of small diameter, and claimed that their result “establishes the asymptotic near-optimality” of the protocol of [S. Kutten, D. Peleg, Fast distributed construction of k-dominating sets and applications, J. Algorithms 28 (1998) 40–66; preliminary version appeared in: Proc. of 14th ACM Symp. on Principles of Distributed Computing, Ottawa, Canada, August 1995, pp. 20–27]. In this paper we refine this claim, and devise a protocol that constructs the MST in Ω˜(μ(G,ω)+n) rounds, where μ(G,ω) is the MST-radius of the graph. The ratio between the diameter and the MST-radius may be as large as Θ(n), and, consequently, on some inputs our protocol is faster than the protocol of [S. Kutten, D. Peleg, Fast distributed construction of k-dominating sets and applications, J. Algorithms 28 (1998) 40–66; preliminary version appeared in: Proc. of 14th ACM Symp. on Principles of Distributed Computing, Ottawa, Canada, August 1995, pp. 20–27] by a factor of Ω˜(n). Also, on every input, the running time of our protocol is never greater than twice the running time of the protocol of [S. Kutten, D. Peleg, Fast distributed construction of k-dominating sets and applications, J. Algorithms 28 (1998) 40–66; preliminary version appeared in: Proc. of 14th ACM Symp. on Principles of Distributed Computing, Ottawa, Canada, August 1995, pp. 20–27]. As part of our protocol for constructing an MST, we develop a protocol for constructing neighborhood covers with a drastically improved running time. The latter result may be of independent interest.