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Minimizing Diameters of Dynamic Trees
 In Proc. 24th International Colloquium on Automata, Languages, and Programming (ICALP
, 1997
"... . In this paper we consider an online problem related to minimizing the diameter of a dynamic tree T . A new edge f is added, and our task is to delete the edge e of the induced cycle so as to minimize the diameter of the resulting tree T [ffgnfeg. Starting with a tree with n nodes, we show how e ..."
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. In this paper we consider an online problem related to minimizing the diameter of a dynamic tree T . A new edge f is added, and our task is to delete the edge e of the induced cycle so as to minimize the diameter of the resulting tree T [ffgnfeg. Starting with a tree with n nodes, we show how each such best swap can be found in worstcase O(log 2 n) time. The problem was raised by Italiano and Ramaswami at ICALP'94 together with a related problem for edge deletions. Italiano and Ramaswami solved both problems in O(n) time per operation. 1 Introduction The diameter of a tree is the length of a longest simple path in the tree and such a path is called a diameter path. The unique midpoint on all diameter paths is called the center, hence the center is the point whose maximal distance to any node is as small as possible. In 1973 Handler [4] showed how one in linear time can compute the diameter (and center) of a tree. However, as pointed out by Rauch [8], too little work has been...
Swapping a failing edge of a single source shortest paths tree is good and fast
 Algorithmica
, 1999
"... Abstract. Let G = (V, E) be a 2edge connected, undirected and nonnegatively weighted graph, and let S(r) be a single source shortest paths tree (SPT) of G rooted at r ∈ V. Whenever an edge e in S(r) fails, we are interested in reconnecting the nodes now disconnected from the root by means of a sing ..."
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Abstract. Let G = (V, E) be a 2edge connected, undirected and nonnegatively weighted graph, and let S(r) be a single source shortest paths tree (SPT) of G rooted at r ∈ V. Whenever an edge e in S(r) fails, we are interested in reconnecting the nodes now disconnected from the root by means of a single edge e ′ crossing the cut created by the removal of e. Such an edge e ′ is named a swap edge for e. Let Se/e ′(r) be the swap tree (no longer an SPT, in general) obtained by swapping e with e ′ , and let Se be the set of all possible swap trees with respect to e. Let F be a function defined over Se that expresses some feature of a swap tree, such as the average length of a path from the root r to all the nodes below edge e, or the maximum length, or one of many others. A best swap edge for e with respect to F is a swap edge f such that F(Se/f (r)) is minimum. In this paper we present efficient algorithms for the problem of finding a best swap edge, for each edge e of S(r), with respect to several objectives. Our work is motivated by a scenario in which individual connections in a communication network suffer transient failures. As a consequence of an edge failure, the shortest paths to all the nodes below the failed edge might completely change, and it might be desirable to avoid an expensive switch to a new SPT, because the failure is only temporary. As an aside, what we get is not even far from a new SPT: our analysis shows that the trees obtained from the swapping have features very similar to those of the corresponding SPTs rebuilt from scratch. Key Words. Network survivability, Single source shortest paths tree, Swap algorithms. 1. Introduction. Survivability
Finding All the Best Swaps of a Minimum Diameter Spanning Tree Under Transient Edge Failures
 Journal of Graph Algorithms and Applications
, 1998
"... Abstract. In network communication systems, frequently messages are routed along a minimum diameter spanning tree (MDST) of the network, to minimize the maximum delay in delivering a message. When a transient edge failure occurs, it is important to choose a temporary replacement edge which minimizes ..."
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Abstract. In network communication systems, frequently messages are routed along a minimum diameter spanning tree (MDST) of the network, to minimize the maximum delay in delivering a message. When a transient edge failure occurs, it is important to choose a temporary replacement edge which minimizes the diameter of the new spanning tree. Such an optimal replacement is called the best swap. As a natural extension, the allbestswaps (ABS) problem is the problem of finding the best swap for every edge of the MDST. Given a weighted graph G =(V, E), where V  = n and E  = m,wesolvetheABSprobleminO(n √ m)time and O(m + n) space, thus improving previous bounds for m = o(n 2). 1
A distributed algorithm for constructing a minimum diameter spanning tree
 J. PARALLEL DISTRIB. COMPUT.
, 2000
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Computing A DiameterConstrained Minimum Spanning Tree
, 2001
"... In numerous practical applications, it is necessary to find the smallest possible tree with a bounded diameter. A diameterconstrained minimum spanning tree (DCMST) of a given undirected, edgeweighted graph, G, is the smallestweight spanning tree of all spanning trees of G which contain no path wi ..."
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Cited by 10 (0 self)
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In numerous practical applications, it is necessary to find the smallest possible tree with a bounded diameter. A diameterconstrained minimum spanning tree (DCMST) of a given undirected, edgeweighted graph, G, is the smallestweight spanning tree of all spanning trees of G which contain no path with more than k edges, where k is a given positive integer. The problem of finding a DCMST is NPcomplete for all values of k; 4 k (n  2), except when all edgeweights are identical. A DCMST is essential for the efficiency of various distributed mutual exclusion algorithms, where it can minimize the number of messages communicated among processors per critical section. It is also useful in linear lightwave networks, where it can minimize interference in the network by limiting the traffic in the network lines. Another practical application requiring a DCMST arises in data compression, where some algorithms compress a file utilizing a tree datastructure, and decompress a path in the tree to access a record. A DCMST helps such algorithms to be fast without sacrificing a lot of storage space. We present a survey of the literature on the DCMST problem, study the expected diameter of a random labeled tree, and present five new polynomialtime algorithms for an approximate DCMST. One of our new algorithms constructs an approximate DCMST in a modified greedy fashion, employing a heuristic for selecting an edge to be added to iii the tree in each stage of the construction. Three other new algorithms start with an unconstrained minimum spanning tree, and iteratively refine it into an approximate DCMST. We also present an algorithm designed for the special case when the diameter is required to be no more than 4. Such a diameter4 tree is also used for evaluating the quality of o...
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, 2002
"... Can users believe what their browsers tell them? Even sophisticated Web users decide whether or not to trust a server based on browser cues such as location bar information, SSL icons, SSL warnings, certificate information, and response time. In their seminal work on Web spoofing, Felten et al [10] ..."
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Can users believe what their browsers tell them? Even sophisticated Web users decide whether or not to trust a server based on browser cues such as location bar information, SSL icons, SSL warnings, certificate information, and response time. In their seminal work on Web spoofing, Felten et al [10] showed how, in 1996, a malicious server could forge some of these cues. However, this work used genuine SSL sessions, and Web technology has evolved much since 1996. The Web has since become the preeminent medium for electronic service delivery to remote users, and the security of many commerce, government, and academic network applications critically rests on the assumption that users can authenticate the servers with which they interact. This situation raises the question: is the browseruser communcation model today secure enough to warrant this assumption? In this paper, we answer this question by systematically showing how a malicious server can forge every one of the above cues. Our work extends the prior results by examining contemporary browsers, and by forging all of the SSL information a client sees, including the very existence of an SSL session (thus providing a cautionary tale about the security of one of the most common applications of PKI). We have made these techniques available for public demonstration, because anything less than working code would not convincingly answer the question. We also discuss implications and potential countermeasures, both shortterm and longterm. 1