Improved Distributed Algorithms for Exact Shortest Paths

Computing shortest paths is one of the central problems in the theory of distributed computing. For the last few years, substantial progress has been made on the approximate single source shortest paths problem, culminating in an algorithm of Becker et al. [DISC'17] which deterministically computes $(1+o(1))$-approximate shortest paths in $\tilde O(D+\sqrt n)$ time, where $D$ is the hop-diameter of the graph. Up to logarithmic factors, this time complexity is optimal, matching the lower bound of Elkin [STOC'04]. The question of exact shortest paths however saw no algorithmic progress for decades, until the recent breakthrough of Elkin [STOC'17], which established a sublinear-time algorithm for exact single source shortest paths on undirected graphs. Shortly after, Huang et al. [FOCS'17] provided improved algorithms for exact all pairs shortest paths problem on directed graphs. In this paper, we present a new single-source shortest path algorithm with complexity $\tilde O(n^{3/4}D^{1/4})$. For polylogarithmic $D$, this improves on Elkin's $\tilde{O}(n^{5/6})$ bound and gets closer to the $\tilde{\Omega}(n^{1/2})$ lower bound of Elkin [STOC'04]. For larger values of $D$, we present an improved variant of our algorithm which achieves complexity $\tilde{O}\left( n^{3/4+o(1)}+ \min\{ n^{3/4}D^{1/6},n^{6/7}\}+D\right)$, and thus compares favorably with Elkin's bound of $\tilde{O}(n^{5/6} + n^{2/3}D^{1/3} + D )$ in essentially the entire range of parameters. This algorithm provides also a qualitative improvement, because it works for the more challenging case of directed graphs (i.e., graphs where the two directions of an edge can have different weights), constituting the first sublinear-time algorithm for directed graphs. Our algorithm also extends to the case of exact $\kappa$-source shortest paths...Comment: 26 page

Clumping towards a UK National catalogue?

This article presents a clumps-oriented perspective on the idea of a UK national catalogue for HE, arguing that a distributed approach based on Z39.50 has a number of attractive features when compared with the alternative physical union catalogue model, but also noting that the many difficulties currently associated with the distributed approach must be resolved before it can itself be regarded as a practical proposition. It is suggested that the distributed model is sufficiently attractive compared to the physical union model to make the expenditure of additional time, effort and resource worthwhile. 'Dynamic clumping' based on collection level description and other appropriate metadata is seen as the key to user navigation in a distributed national catalogue. Large physical union catalogues like COPAC are assumed to have a role, although updating difficulties and the lack of circulation information may limit its scope

Distributed Processes, Distributed Cognizers and Collaborative Cognition

Cognition is thinking; it feels like something to think, and only those who can feel can think. There are also things that thinkers can do. We know neither how thinkers can think nor how they are able do what they can do. We are waiting for cognitive science to discover how. Cognitive science does this by testing hypotheses about what processes can generate what doing (“know-how”) This is called the Turing Test. It cannot test whether a process can generate feeling, hence thinking -- only whether it can generate doing. The processes that generate thinking and know-how are “distributed” within the heads of thinkers, but not across thinkers’ heads. Hence there is no such thing as distributed cognition, only collaborative cognition. Email and the Web have spawned a new form of collaborative cognition that draws upon individual brains’ real-time interactive potential in ways that were not possible in oral, written or print interactions

Distributed utterances

I propose an apparatus for handling intrasentential change in context. The standard approach has problems with sentences with multiple occurrences of the same demonstrative or indexical. My proposal involves the idea that contexts can be complex. Complex contexts are built out of (“simple”) Kaplanian contexts by ordered n-tupling. With these we can revise the clauses of Kaplan’s Logic of Demonstratives so that each part of a sentence is taken in a different component of a complex context. I consider other applications of the framework: to agentially distributed utterances (ones made partly by one speaker and partly by another); to an account of scare-quoting; and to an account of a binding-like phenomenon that avoids what Kit Fine calls “the antinomy of the variable.

Distributed XQuery

XQuery is increasingly being used for ad-hoc integration of heterogeneous data sources that are logically mapped to XML. For example, scientists need to query multiple scientific databases, which are distributed over a large geographic area, and it is possible to use XQuery for that. However, the language currently supports only the data shipping query evaluation model (through the document() function): it fetches all data sources to a single server, then runs the query there. This is a major limitation for many applications, especially when some data sources are very large, or when a data source is only a virtual XML view over some other logical data model. We propose here a simple extension to XQuery that allows query shipping to be expressed in the language, in addition to data shipping

Distributed Teaching

The central phenomenon that this entry seeks to explore is that people with the job title of “teacher” are almost never the only teachers in a learning transaction, and autodidacts are almost never solely responsible for their own learning. As well as designated teachers and students, text book authors, editors, illustrators, exam boards, curriculum designers, governments, timetablers, classroom designers, architects, learning management system managers, counselors, career advisors, makers of YouTube videos, discussion forums, friends, family, and very many other individuals and groups can and do play an active and often highly significant teaching role in guiding, supporting, and managing the learning process. Online learning, especially when it involves a team of specialists working on a course, makes the distributed nature of the process very visible, and the relative autonomy of online learners makes it more likely that they will seek additional or alternative supports for learning, but virtually all conventional in-person teaching involves multiple teachers too, from peers to textbook authors and, most especially, the learners themselves

Distributed quantum computing: A distributed Shor algorithm

We present a distributed implementation of Shor's quantum factoring algorithm on a distributed quantum network model. This model provides a means for small capacity quantum computers to work together in such a way as to simulate a large capacity quantum computer. In this paper, entanglement is used as a resource for implementing non-local operations between two or more quantum computers. These non-local operations are used to implement a distributed factoring circuit with polynomially many gates. This distributed version of Shor's algorithm requires an additional overhead of O((log N)^2) communication complexity, where N denotes the integer to be factored.Comment: 13 pages, 12 figures, extra figures are remove