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217
Navigating nets: Simple algorithms for proximity search (Extended Abstract)
, 2004
"... Robert Krauthgamer # James R. Lee + Abstract We present a simple deterministic data structure for maintaining a set S of points in a general metric space, while supporting proximity search (nearest neighbor and range queries) and updates to S (insertions and deletions). Our data structure consists ..."
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Cited by 154 (18 self)
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Robert Krauthgamer # James R. Lee + Abstract We present a simple deterministic data structure for maintaining a set S of points in a general metric space, while supporting proximity search (nearest neighbor and range queries) and updates to S (insertions and deletions). Our data structure
Approximating the Minimum Bisection Size (extended Abstract)
, 2000
"... ) Uriel Feige Robert Krauthgamer Kobbi Nissim Deptartment of Computer Science and Applied Mathematics Weizmann Institute of Science Rehovot 76100, Israel ffeige,robi,kobbig@wisdom.weizmann.ac.il February 22, 2000 Abstract A bisection of a graph with n vertices is a partition of its vertices ..."
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Cited by 4 (0 self)
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) Uriel Feige Robert Krauthgamer Kobbi Nissim Deptartment of Computer Science and Applied Mathematics Weizmann Institute of Science Rehovot 76100, Israel ffeige,robi,kobbig@wisdom.weizmann.ac.il February 22, 2000 Abstract A bisection of a graph with n vertices is a partition of its vertices
is intuition.
"... I would like to express my deep appreciation and my sincere gratitude to my Masters thesis advisor, Prof. Robert Krauthgamer, for his kindly and patient guidance, friendly support and for his devoted attention. It was a pleasure to work and to be inspired by him. I would like to thank my fellow stud ..."
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I would like to express my deep appreciation and my sincere gratitude to my Masters thesis advisor, Prof. Robert Krauthgamer, for his kindly and patient guidance, friendly support and for his devoted attention. It was a pleasure to work and to be inspired by him. I would like to thank my fellow
Approximating the Bandwidth Via Volume Respecting Embeddings
, 1999
"... A linear arrangement of an nvertex graph is a onetoone mapping of its vertices to the integers f1; : : : ; ng. The bandwidth of a linear arrangement is the maximum difference between mapped values of adjacent vertices. The problem of finding a linear arrangement with smallest possible bandwidt ..."
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Cited by 105 (3 self)
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A linear arrangement of an nvertex graph is a onetoone mapping of its vertices to the integers f1; : : : ; ng. The bandwidth of a linear arrangement is the maximum difference between mapped values of adjacent vertices. The problem of finding a linear arrangement with smallest possible bandwidth in NPhard. We present a randomized algorithm that runs in nearly linear time and outputs a linear arrangement whose bandwidth is within a polylogarithmic multiplicative factor of optimal. Our algorithm is based on a new notion, called volume respecting embeddings, which is a natural extension of small distortion embeddings of Bourgain and of Linial, London and Rabinovich. 1 Introduction We consider the problem of minimizing the bandwidth of an undirected connected graph G(V; E), where n = jV j and m = jEj. One needs to find a linear arrangement of the vertices, namely, a onetoone mapping f : V \Gamma! f1; 2; : : : ng, for which the bandwidth, i.e. max (i;j)2E jf(i) \Gamma f(j)j, i...
On the Hardness of Approximating Multicut and SparsestCut
 In Proceedings of the 20th Annual IEEE Conference on Computational Complexity
, 2005
"... We show that the MULTICUT, SPARSESTCUT, and MIN2CNF ≡ DELETION problems are NPhard to approximate within every constant factor, assuming the Unique Games Conjecture of Khot [STOC, 2002]. A quantitatively stronger version of the conjecture implies inapproximability factor of Ω(log log n). 1. ..."
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Cited by 102 (5 self)
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We show that the MULTICUT, SPARSESTCUT, and MIN2CNF ≡ DELETION problems are NPhard to approximate within every constant factor, assuming the Unique Games Conjecture of Khot [STOC, 2002]. A quantitatively stronger version of the conjecture implies inapproximability factor of Ω(log log n). 1.
How Did Dread Pirate Roberts Acquire and Protect His Bitcoin Wealth
 In 1st Workshop on Bitcoin Research
, 2014
"... Abstract. The Bitcoin scheme is one of the most popular and talked about alternative payment schemes. One of the most active parts of the Bitcoin ecosystem was the Silk Road marketplace, in which highly illegal substances and services were traded. It was run by a person who called himself Dread Pira ..."
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Cited by 1 (0 self)
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Pirate Roberts (DPR), whose bitcoin holdings are estimated to be worth hundreds of millions of dollars at today’s exchange rate. On October 1st 2013, the FBI arrested a 29 year old person named Ross William Ulbricht, claiming that he is DPR, and seizing a small fraction of his bitcoin wealth
Lower bounds on streaming algorithms for approximating the length of the longest increasing subsequence
 In Proc. FOCS’07
, 2007
"... We show that any deterministic datastream algorithm that makes a constant number of passes over the input and gives a constant factor approximation of the length of the longest increasing subsequence in a sequence of length n must use space Ω ( √ n). This proves a conjecture made by Gopalan, Jayra ..."
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Cited by 13 (0 self)
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, Jayram, Krauthgamer and Kumar [GJKK07] who proved a matching upper bound. Our results yield asymptotically tight lower bounds for all approximation factors, thus resolving the main open problem from their paper. Our proof is based on analyzing a related communication problem and proving a direct sum type
Integrality ratio for group steiner trees and directed steiner trees
 In 14th Annual ACMSIAM Symposium on Discrete Algorithms
, 2003
"... The natural relaxation for the Group Steiner Tree problem, as well as for its generalization, the Directed Steiner Tree problem, is a flowbased linear programming relaxation. We prove new lower bounds on the integrality ratio of this relaxation. For the Group Steiner Tree problem, we show the integ ..."
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Cited by 29 (6 self)
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, for the first time, a relaxation of a natural optimization problem whose integrality ratio is known to be superlogarithmic but subpolynomial. Our results and techniques have been used by Halperin and Krauthgamer [Symp. on Theory of Computing, pp. 585–594, 2003] to show comparable inapproximability results
Overcoming the ℓ1 nonembeddability barrier: Algorithms for product metrics
, 2008
"... A common approach for solving computational problems over a difficult metric space is to embed the “hard ” metric into L1, which admits efficient algorithms and is thus considered an “easy ” metric. This approach has proved successful or partially successful for important spaces such as the edit dis ..."
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Cited by 18 (8 self)
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]. One of our algorithms has already found applications for smoothed edit distance over 01 strings [Andoni and Krauthgamer, ICALP 2008]. 1
Quantitative Analysis of the Full Bitcoin Transaction Graph
"... Abstract. The Bitcoin scheme is a rare example of a large scale global payment system in which all the transactions are publicly accessible (but in an anonymous way). We downloaded the full history of this scheme, and analyzed many statistical properties of its associated transaction graph. In this ..."
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Cited by 46 (1 self)
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Abstract. The Bitcoin scheme is a rare example of a large scale global payment system in which all the transactions are publicly accessible (but in an anonymous way). We downloaded the full history of this scheme, and analyzed many statistical properties of its associated transaction graph. In this paper we answer for the first time a variety of interesting questions about the typical behavior of users, how they acquire and how they spend their bitcoins, the balance of bitcoins they keep in their accounts, and how they move bitcoins between their various accounts in order to better protect their privacy. In addition, we isolated all the large transactions in the system, and discovered that almost all of them are closely related to a single large transaction that took place in November 2010, even though the associated users apparently tried to hide this fact with many strange looking long chains and forkmerge structures in the transaction graph.
Results 1  10
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