1

December 2017
ACM Transactions on Computation Theory (TOCT): Volume 9 Issue 4, January 2018

**Publisher:** ACM

**Bibliometrics**:

Citation Count: 0

Downloads (6 Weeks): 9, Downloads (12 Months): 9, Downloads (Overall): 9

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Consider the problem of finding a point in a metric space ({ 1,2,&ldots;, n }, d ) with the minimum average distance to other points. We show that this problem has no deterministic o ( n 1+1/( h −1) / h )-query 2 h ċ (1-ε))-approximation algorithms for any constant ...

**Keywords**:
1-median selection, sublinear-query computation, closeness centrality, metric space

2

March 2017
Journal of Computer and System Sciences: Volume 84 Issue C, March 2017

**Publisher:** Academic Press, Inc.

Consider the problem of finding a point in an n-point metric space with the minimum average distance to all points. We show that this problem has no deterministic o ( n 2 ) -query ( 4 - ź ) -approximation algorithms for any constant ź 0 . Given oracle access ...

**Keywords**:
Metric space, Query complexity, 1-Median selection, Sublinear-query algorithm, Sublinear-time algorithm

3

October 2015
Theoretical Computer Science: Volume 602 Issue C, October 2015

**Publisher:** Elsevier Science Publishers Ltd.

We give a deterministic O ( h n 1 + 1 / h ) -time ( 2 h ) -approximation nonadaptive algorithm for 1-median selection in n-point metric spaces, where h � Z + � { 1 } is arbitrary. Our proof generalizes that of Chang 2.

**Keywords**:
1-Median selection, Sublinear-time algorithm, k-Median selection, Closeness centrality, Metric space

4

August 2015
Theoretical Computer Science: Volume 593 Issue C, August 2015

**Publisher:** Elsevier Science Publishers Ltd.

Consider the following process of activation on a strongly connected directed graph G ( V , E ) with threshold function � : V � N . In round zero, a set of vertices, called the seeds, are active. Thereafter, a vertex v � V is activated in a round ...

**Keywords**:
Bootstrap percolation, Irreversible dynamic monopoly, Perfect target set, Watts' model

5

January 2014
Discrete Applied Mathematics: Volume 162 Issue C, January 2014

**Publisher:** Elsevier Science Publishers B. V.

We show that each randomized o ( | G | 2 ) -query algorithm can recover only an expected o ( 1 ) fraction of the Cayley table of some finite Abelian loop ( G , � ) , where both multiplication and inversion queries are allowed. Furthermore, each randomized ...

**Keywords**:
Loop, Monoid, Semiring, Query complexity

6

January 2014
Discrete Applied Mathematics: Volume 162, January, 2014

**Publisher:** Elsevier Science Publishers B. V.

We show that each randomized o(|G|^2)-query algorithm can recover only an expected o(1) fraction of the Cayley table of some finite Abelian loop (G,@?), where both multiplication and inversion queries are allowed. Furthermore, each randomized o(|R|^2)-query algorithm can recover only an expected o(1) fraction of any of the Cayley tables ...

**Keywords**:
Query complexity, Loop, Monoid, Semiring

7

February 2013
Theory of Computing Systems: Volume 52 Issue 2, February 2013

**Publisher:** Springer-Verlag New York, Inc.

Consider the following cascading process on a simple undirected graph G ( V , E ) with diameter Δ. In round zero, a set S � V of vertices, called the seeds, are active. In round i +1, i ��, a non-isolated vertex is activated if at least a � ...

**Keywords**:
Global cascade, Local interaction game, Reversible dynamic monopoly, Fault propagation, Repetitive polling game, Static monopoly

8

January 2013
Theoretical Computer Science: Volume 468, January, 2013

**Publisher:** Elsevier Science Publishers Ltd.

Consider the following reversible cascade on a simple directed graph G=(V,E). In round zero, a set of vertices, called the seeds, are active. In round

[email protected]?Z^+, a vertex

[email protected]?V is activated (deactivated) if at least (resp., fewer than) @f(v) of its in-neighbors are active in round k-1, where @f:V->N. An ...

9

April 2012
Theoretical Computer Science: Volume 426-427, April, 2012

**Publisher:** Elsevier Science Publishers Ltd.

A 1-median in a finite metric space is a point with the minimum average distance to all other points. Given a positive integer n and oracle access to a distance metric on {1,2,...,n}, we study the problem of finding a 1-median. In particular, we show the nonexistence of (1) deterministic ...

**Keywords**:
1-median, Closeness centrality, Metric space, Query complexity

10

October 2011
Information Processing Letters: Volume 111 Issue 19, October, 2011

**Publisher:** Elsevier North-Holland, Inc.

Consider the following cascading process on an undirected connected graph G(V,E). A set S of vertices, called the seeds, are active initially. Thereafter, an inactive vertex is activated when at least a @r fraction of its neighbors is active, where @

[email protected]?(0,1]. The cascading process proceeds asynchronously until no more vertices ...

**Keywords**:
Fault propagation, Irreversible dynamic monopoly, Repetitive polling game, Watts' model, Fault tolerance, Irreversible conversion set, Local interaction game, Reversible dynamic monopoly

11

July 2011
IWOCA'11: Proceedings of the 22nd international conference on Combinatorial Algorithms

**Publisher:** Springer-Verlag

Consider the following reversible cascade on the Erdős-Rényi random graph G ( n , p ). In round zero, a set of vertices, called the seeds, are active. For a given ρ ∈( 0,1 ], a non-isolated vertex is activated (resp., deactivated) in round t ∈ℤ + if the fraction ...

12

February 2011
Theory of Computing Systems: Volume 48 Issue 2, February 2011

**Publisher:** Springer-Verlag New York, Inc.

Consider the following model on the spreading of messages. A message initially convinces a set of vertices, called the seeds, of the Erdős-Rényi random graph G ( n , p ). Whenever more than a ρ ∈(0,1) fraction of a vertex v ’s neighbors are convinced of the message, v ...

**Keywords**:
Fault propagation, Global cascades

13

May 2010
CIAC'10: Proceedings of the 7th international conference on Algorithms and Complexity

**Publisher:** Springer-Verlag

Consider the following coloring process in a simple directed graph G ( V , E ) with positive indegrees. Initially, a set S of vertices are white. Thereafter, a black vertex is colored white whenever the majority of its in-neighbors are white. The coloring process ends when no additional vertices ...

14

March 2010
Theoretical Computer Science: Volume 411 Issue 16-18, March, 2010

**Publisher:** Elsevier Science Publishers Ltd.

The Banach fixed-point theorem states that a contraction mapping on a complete metric space has a unique fixed point. Given an oracle access to a finite metric space (M,d) and a contraction mapping f:M->M on it, we show that the fixed point of f can be found with an expected ...

**Keywords**:
Caristi-Kirk fixed-point theorem, Contraction mapping principle, Banach fixed-point theorem, Query complexity

15

June 2009
Theoretical Computer Science: Volume 410 Issue 27-29, June, 2009

**Publisher:** Elsevier Science Publishers Ltd.

We model a network in which messages spread by a simple directed graph G=(V,E) and a function @a:V->N mapping each

[email protected]?V to a positive integer less than or equal to the indegree of v. The graph G represents the individuals in the network and the communication channels between them. An ...

**Keywords**:
Irreversible dynamo, Trust propagation, Global cascade

16

January 2009
CATS '09: Proceedings of the Fifteenth Australasian Symposium on Computing: The Australasian Theory - Volume 94

**Publisher:** Australian Computer Society, Inc.

**Bibliometrics**:

Citation Count: 1

Downloads (6 Weeks): 1, Downloads (12 Months): 4, Downloads (Overall): 31

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Chang and Lyuu [Chang and Lyuu, 2008] study the spreading of a message in an Erdős-Rényi random graph G ( n, p ) starting from a set of vertices that are convinced of the message initially. In their strict-majority scenario, whenever more than half of the neighbors of a vertex ...

17

July 2008
Theoretical Computer Science: Volume 401 Issue 1-3, July, 2008

**Publisher:** Elsevier Science Publishers Ltd.

Tarski's fixed point theorem guarantees the existence of a fixed point of an order-preserving function f:L->L defined on a nonempty complete lattice (L,@?) [B. Knaster, Un theoreme sur les fonctions d'ensembles, Annales de la Societe Polonaise de Mathematique 6 (1928) 133-134; A. Tarski, A lattice theoretical fixpoint theorem and its ...

**Keywords**:
Query complexity, Tarski's fixed point theorem

18

June 2008
COCOON '08: Proceedings of the 14th annual international conference on Computing and Combinatorics

**Publisher:** Springer-Verlag

We model a network in which messages spread by a simple directed graph <em>G</em>= (<em>V</em>,<em>E</em>) [8] and a function <em></em>: <em>V</em> mapping each <em>v</em> <em>V</em>to a positive integer less than or equal to the indegree of <em>v</em>. The graph <em>G</em>represents the individuals in the network and the communication channels between ...

19

January 2008
CATS '08: Proceedings of the fourteenth symposium on Computing: the Australasian theory - Volume 77

**Publisher:** Australian Computer Society, Inc.

**Bibliometrics**:

Citation Count: 0

Downloads (6 Weeks): 0, Downloads (12 Months): 3, Downloads (Overall): 35

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Let L ≥ 1, ε> 0 be real numbers, ( M, d ) be a finite metric space and ( N, ρ ) be a metric space (Rudin 1976). The metric space ( M, d ) is said to be L -bilipschitz embeddable into ( N, ρ ) if there ...

20

July 2007
COCOON'07: Proceedings of the 13th annual international conference on Computing and Combinatorics

**Publisher:** Springer-Verlag

Each day a weather forecaster predicts a probability of each type of weather for the next day. After n days, all the predicted probabilities and the real weather data are sent to a test which decides whether to accept the forecaster as possessing predicting power. Consider tests such that forecasters ...