Showing papers by "Evangelos Kranakis published in 2000"
TL;DR: For points in three dimensions it is shown that the problem of deciding whether a complete range assignment of a given cost exists, is NP-hard and an O(n 2 ) time approximation algorithm is given which provides a completerange assignment with cost within a factor of two of the minimum.
468 citations
18 Dec 2000
TL;DR: This work gives algorithms for assigning hotlinks, as well as upper and lower bounds on the expected number of steps to reach the leaves from the source page s located at the root of a complete binary tree.
Abstract: Consider a DAG (directed acyclic graph) G = (V, E) representing a collection V of web pages connected via links E All web pages can be reached from a designated source page, represented by a source node s of G Each web page carries a weight representative of the frequency with which it is visited By adding hotlinks, at most one per page, we are interested in minimizing the expected number of steps needed to visit a selected set of web pages from the source page For arbitrary DAGs we show that the problem is NP-complete
We also give algorithms for assigning hotlinks, as well as upper and lower bounds on the expected number of steps to reach the leaves from the source page s located at the root of a complete binary tree Depending on the probability distribution (arbitrary, uniform, Zipf) the expected number of steps is at most c ċ n, where c is a constant less than 1 For the geometric distribution we show how to obtain a constant average number of steps
52 citations
TL;DR: This work considers the problem of adaptive fault diagnosis in hypercube multiprocessor systems and proposes an adaptive diagnosis algorithm whose efficiency is drastically better than that of any previously known strategies.
Abstract: We consider the problem of adaptive fault diagnosis in hypercube multiprocessor systems. Processors perform tests on one another and later tests can be scheduled on the basis of previous test results. Fault-free testers correctly identify the fault status of tested processors, while faulty testers can give arbitrary test results. The goal is to identify correctly the status of all processors, assuming that the number of faults does not exceed the hypercube dimension. We propose an adaptive diagnosis algorithm whose efficiency is drastically better than that of any previously known strategies. While the worst-case number of tests for any of them exceeds 2/sup n/ log n for an n-dimensional hypercube, our method uses at most 2/sup n/+3n/2 tests in the worst case. We can also modify our algorithm to improve the number of testing rounds. By slightly increasing the number of tests to 2/sup n/+(n+1)/sup 2/ (still a much better performance than 2/sup n/ log n), we can carry out diagnosis in at most 11 rounds in the worst case (as opposed to over n rounds in the best previously known strategy).
37 citations
04 Oct 2000
TL;DR: This paper provides algorithms for locating an information nodes in the complete communication network, that take advantage of advice given from network nodes, and proves that no fixed memory deterministic algorithm can locate the information node in finite expected number of steps.
Abstract: We consider the problem of searching for a piece of information in a fully interconnected computer network (or clique) by exploiting advice about its location from the network nodes. Each node contains a database that "knows" what kind of documents or information are stored in other nodes (e.g. a node could be a Web server that answers queries about documents stored on the Web). The databases in each node, when queried, provide a pointer that leads to the node that contains the information. However, this information is up-to-date (or correct) with some bounded probability. While, in principle, one may always locate the information by simply visiting the network nodes in some prescribed ordering, this requires a time complexity in the order of the number of nodes of the network. In this paper, we provide algorithms for locating an information node in the complete communication network, that take advantage of advice given from network nodes. The nodes may either give correct advice, by pointing directly to the information node, or give wrong advice by pointing elsewhere. We show that, on the average, if the probability p that a node provides correct advice is asymptotically larger than 1/n, where n is the number of the computer nodes, then the average time complexity for locating the information node is, asymptotically, 1/p or 2/p depending on the available memory. The probability p may, in general, be a function of the number of network nodes n. On the lower bounds side, we prove that no fixed memory deterministic algorithm can locate the information node in finite expected number of steps. We also prove a lower bound of 1/p for the expected number of steps of any algorithm that locates the information node in the complete network.
21 citations
TL;DR: In this paper, the minimum number of pieces needed to dissect a regular m-gon into a regular n-gon of the same area using polygonal cuts was studied and it was shown that ⌈n/4⌉ ≤ p(4, n) ≤ (n/2 + o(n)) holds for sufficiently large n.
Abstract: We study the minimum number g(m, n) (respectively, p(m, n)) of pieces needed to dissect a regular m-gon into a regular n-gon of the same area using glass-cuts (respectively, polygonal cuts). First we study regular polygon-square dissections and show that ⌈n/2⌉ - 2 ≤ g(4, n) ≤ (n/2) + o(n) and ⌈n/4⌉ ≤ g(n, 4) ≤ (n/2) + o(n) hold for sufficiently large n. We also consider polygonal cuts, i.e., the minimum number p(4, n) of pieces needed to dissect a square into a regular n-gon of the same area using polygonal cuts and show that ⌈n/4⌉ ≤ p(4, n) ≤ (n/2) + o(n) holds for sufficiently large n. We also consider regular polygon-polygon dissections and obtain similar bounds for g(m, n) and p(m, n).
12 citations
29 Aug 2000
TL;DR: Algorithms to search for an item s contained in a node of a network, without prior knowledge of its exact location are presented, which consider the complete graph, ring, torus, hypercube and bounded degree trees.
Abstract: In this paper, we present algorithms to search for an item s contained in a node of a network, without prior knowledge of its exact location. Each node of the network has a database that will answer queries of the form "how do I get to s?" by responding with the first edge on a shortest path to s. It may happen that some nodes, called liars, give bad advice. If the number of liars k is bounded, we show different strategies to find the item depending on the topology of the network. In particular we consider the complete graph, ring, torus, hypercube and bounded degree trees.
8 citations
Proceedings Article•
01 Jan 2000
TL;DR: An adjustable bearing assembly has radial and thrust bearings adjustable on a bearing shaft to eliminate clearance in the bearings and in springs in the bearing assembly in combination with an in-hole motor of the fluid driven type.
Abstract: An adjustable bearing assembly has radial and thrust bearings adjustable on a bearing shaft to eliminate clearance in the bearings and in springs in the bearing assembly. The bearing assembly is shown in combination with an in-hole motor of the fluid driven type. Components driven by the shaft are locked on the shaft by an eccentric surface or a combination of an eccentric and a concentric surface.
8 citations
01 May 2000
TL;DR: This paper considers the problem of sorting such a distributed multiset and investigates its relationship with the election problem, providing strong characterizations, showing lower bounds, and establishing efficient upper bounds.
Abstract: An anonymous ring network is a ring where all processors (vertices) are totally indistinguishable except for their input value. Initially, to each vertex of the ring is associated a value from a totally ordered set; thus, forming a multiset. In this paper we consider the problem of sorting such a distributed multiset and we investigate its relationship with the election problem. We focus on the computability and the complexity of these problems, as well as on their interrelationship, providing strong characterizations, showing lower bounds, and establishing efficient upper bounds.
8 citations
TL;DR: New upper and lower bounds on the bit complexity of string recognition are given and it is shown that almost all strings can be recognized by communicating Θ (n log n) bits.
Abstract: We consider the problem of recognizing whether a given binary string of length n is equal (up to rotation) to the input of an anonymous oriented ring of n processors. Previous algorithms for this problem have been ``global'' and do not take into account ``local'' patterns occurring in the string. In this paper we give new upper and lower bounds on the bit complexity of string recognition. For periodic strings, near optimal bounds are given which depend on the period of the string. For Kolmogorov random strings an optimal algorithm is given. As a consequence, we show that almost all strings can be recognized by communicating Θ (n log n) bits. It is interesting to note that Kolmogorov complexity theory is used in the proof of our upper bound, rather than its traditional application to the proof of lower bounds.
5 citations