SIAM Journal on Computing, 2(1):1-6, March 1973. (2008)
Dimitris Achlioptas, Sheldon B. Akers, Noga Alon
[3] E. A. Akkoyunlu. The enumeration of maximal cliques of large graphs.
Dimitris Achlioptas, David Kempe, Aaron Clauset
Understanding the structure of the Internet graph is a crucial step for building accurate network models and designing efficient algorithms for Internet applications. Yet, obtaining its graph...
Dimitris Achlioptas, David Kempe, Aaron Clauset
Understanding the structure of the Internet graph is a crucial step for building accurate network models and designing efficient algorithms for Internet applications. Yet, obtaining its graph...
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Dimitris Achlioptas, Frank Mcsherry, Bernhard Schölkopf
We propose randomized techniques for speeding up Kernel Principal Component Analysis on three levels: sampling and quantization of the Gram matrix in training, randomized rounding in evaluating the...
Dimitris Achlioptas, Frank Mcsherry
We consider the problem of learning mixtures of distributions via spectral methods and derive a tight characterization of when such methods are useful. Specifically, given a mixture-sample, let µ i,...
Dimitris Achlioptas, Frank Mcsherry
Given a matrix A, it is often desirable to find a good approximation to A that has low rank. We introduce a simple technique for accelerating the computation of such approximations when A has strong...
Algorithmic barriers from phase transitions (2008)
Achlioptas, Dimitris, Coja-Oghlan, Amin
For many random Constraint Satisfaction Problems, by now, we have asymptotically tight estimates of the largest constraint density for which they have solutions. At the same time, all known...
Dimitris Achlioptas, Frank Mcsherry, Bernhard Schölkopf
We propose randomized techniques for speeding up Kernel Principal Component Analysis on three levels: sampling and quantization of the Gram matrix in training, randomized rounding in evaluating the...
A Sharp Threshold in Proof Complexity Yields Lower Bounds for (2008)
Satisfiability Search Dimitris, Dimitris Achlioptas, Michael Molloy, Paul Beame
Let F (#n, #n) denote a random CNF formula consisting of #n randomly chosen 2-clauses and #n randomly chosen 3-clauses, for some arbitrary constants #, # 0. It is well-known that, with probability...
On Spectral Learning of Mixtures of Distributions (2008)
Dimitris Achlioptas, Frank Mcsherry
We consider the problem of learning mixtures of distributions via spectral methods and derive a tight characterization of when such methods are useful. Specifically, given a mixture-sample, let i , C...
Dimitris Achlioptas, Amos Fiat, Anna R. Karlin, Frank Mcsherry. Web, In Moni Naor, Proceedings Of The
[2] Nasreen AbdulJaleel and Yan Qu. Domain term extraction and struc-turing via link analysis. In Dunja Mladenic, Natasha Milic-Frayling, and
Rigorous Results for Random (2+p)-SAT (2007)
Dimitris Achlioptas, Lefteris M. Kirousis, Evangelos Kranakis, Danny Krizanc
In recent years there has been significant interest in the study of random k-SAT fomulae. For a given set of n Boolean variables, let B k denote the set of all possible disjunctions of k distinct,...
Jeff Edmonds, Chung Keung Poon, Dimitris Achlioptas, Society For Industrial
. Directed st-connectivity is the problem of deciding whether or not there exists a path from a distinguished node s to a distinguished node t in a directed graph. We prove a time-- space lower bound...
Dimitris Achlioptas, Yuval Peres
Let Fk (n, m) be a random k-SAT formula with n variables and m clauses selected uniformly and independently among all 2 k
--- William Shakespeare, Loves Labours Lost. Act i. Sc. 1. (2007)
Dimitris Achlioptas, Anna R. Karlin, Frank Mcsherry
Small have continual plodders ever won save base authority from others books.
In many practical applications, given an m n matrix A it is of interest to nd an approximation to A that has low rank. We introduce a technique that exploits spectral structure in A to accelerate...
Dimitris Achlioptas, Paul Beame, Michael Molloy
sharp threshold in proof complexity yields lower bounds for
--- William Shakespeare, Loves Labours Lost. Act i. Sc. 1. (2007)
Dimitris Achlioptas, Anna R. Karlin, Frank Mcsherry
Small have continual plodders ever won save base authority from others books.
Dimitris Achlioptas, Jeong Han Kim, Michael Krivelevich, Prasad Tetali
A 2-coloring of a hypergraph is a mapping from its vertex set to a set of two colors such that no edge is monochromatic. Let H = H(k; n; p) be a random k-uniform hypergraph on a vertex set V of...
Dimitris Achlioptas, Paul Beame, Michael Molloy
sharp threshold in proof complexity yields lower bounds for
The two possible values of the chromatic number of a random graph (2007)
Achlioptas, Dimitris, Naor, Assaf
Given d \in (0,infty) let k_d be the smallest integer k such that d < 2k\log k. We prove that the chromatic number of a random graph G(n,d/n) is either k_d or k_d+1 almost surely.
On the Solution-Space Geometry of Random Constraint Satisfaction Problems (2006)
Achlioptas, Dimitris, Ricci-Tersenghi, Federico
For a large number of random constraint satisfaction problems, such as random k-SAT and random graph and hypergraph coloring, there are very good estimates of the largest constraint density for which...
Marko Grobelink, Daniel M. Abrams, Dimitris Achlioptas, Aaron Clauset, David Kempe
[2] Nasreen AbdulJaleel and Yan Qu. Domain term extraction and structuring via link analysis. In Dunja Mladenic, Natasha Milic-Frayling, and
On the solution-space geometry of random constraint satisfaction problems (2006)
Dimitris Achlioptas, Federico Ricci-tersenghi
For a large number of random constraint satisfaction problems, such as random k-SAT and random graph and hypergraph coloring, there are very good estimates of the largest constraint density for which...
Dimitris Achlioptas, David Kempe, Aaron Clauset, Cristopher Moore
Understanding the structure of the Internet graph is a crucial step for building accurate network models and designing efficient algorithms for Internet applications. Yet, obtaining its graph...
Random k-SAT: two moments suffice to cross a sharp threshold (2006)
Dimitris Achlioptas, Cristopher Moore
Abstract. Many NP-complete constraint satisfaction problems appear to undergo a “phase transition” from solubility to insolubility when the constraint density passes through a critical threshold....
The two possible values of the chromatic number of a random graph (2005)
Achlioptas, Dimitris, Naor, Assaf
Given $d \in (0,\infty)$ let $k_d$ be the smallest integer $k$ such that $d
Rapid Mixing for Lattice Colorings with Fewer Colors (2005)
Achlioptas, Dimitris, Molloy, Michael, Moore, Cristopher, Van Bussell, Frank
We provide an optimally mixing Markov chain for 6-colorings of the square lattice on rectangular regions with free, fixed, or toroidal boundary conditions. This implies that the uniform distribution...
Hiding Satisfying Assignments: Two are Better than One (2005)
Achlioptas, Dimitris, Jia, Haixia, Moore, Cristopher
The evaluation of incomplete satisfiability solvers depends critically on the availability of hard satisfiable instances. A plausible source of such instances consists of random k-SAT formulas whose...
On the Bias of Traceroute Sampling; or, Power-law Degree Distributions in Regular Graphs (2005)
Achlioptas, Dimitris, Clauset, Aaron, Kempe, David, Moore, Cristopher
Understanding the structure of the Internet graph is a crucial step for building accurate network models and designing efficient algorithms for Internet applications. Yet, obtaining its graph...
The two possible values of the chromatic number of a random graph (2005)
Achlioptas, Dimitris, Naor, Assaf
Given d ¿¿ (0,¿¿) let kd be the smallest integer k such that d < 2k log k. We prove that the chromatic number of a random graph G(n, d/n) is either kd or kd + 1 almost surely.
Journal of Statistical Mechanics: An IOP and SISSA journal Theory and Experiment (2005)
Dimitris Achlioptas, Cristopher Moore, Frank Van Bussel
Rapid mixing for lattice colourings with fewer colours
The Chromatic Number of Random Regular Graphs (2004)
Achlioptas, Dimitris, Moore, Cristopher
Given any integer d >= 3, let k be the smallest integer such that d < 2k log k. We prove that with high probability the chromatic number of a random d-regular graph is k, k+1, or k+2, and that if...
Summary-based Routing for Content-based Event Distribution Networks (2004)
Yi-min Wang, Lili Qiu, Chad Verbowski, Dimitris Achlioptas, Gautam Das, Paul Larson
Abstract — Providing scalable distributed Web-based eventing services has been an important research topic. It is desirable to have an effective mechanism for the servers to summarize their filters...
The chromatic number of random regular graphs (2004)
Dimitris Achlioptas, Cristopher Moore
Abstract. Given any integer d ≥ 3, let k be the smallest integer such that d < 2k log k. We prove that with high probability the chromatic number of a random d-regular graph is k, k + 1, or k +...
Hiding satisfying assignments: two are better than one (2004)
Dimitris Achlioptas, Haixia Jia, Cristopher Moore
The evaluation of incomplete satisfiability solvers depends critically on the availability of hard satisfiable instances. A plausible source of such instances consists of random k-SAT formulas whose...
The two possible values of the chromatic number of a random graph (2004)
Dimitris Achlioptas, Assaf Naor
Abstract Given d 2 (0, 1) let kd be the smallest integer k such that d < 2k log k. We prove that thechromatic number of a random graph G(n, d/n) is either kd or kd + 1 almost surely. 1...
Exponential Bounds for DPLL below the Satisfiability Threshold (2004)
Dimitris Achlioptas, Paul Beame, Michael Molloy
We prove that for every k 4 there exists a constant r k such that a random k-CNF formula F with n variables and #r k n# clauses is satisfiable with high probability, but every backtracking extension...
The Threshold for Random k-SAT is 2^k log 2 - O(k) (2004)
Dimitris Achlioptas, Yuval Peres
this paper. We also thank the referees for useful comments. Part of this work was done while the authors participated in the focused research group on discrete probability at BIRS, July 12-26, 2003
The Chromatic Number of Random Regular Graphs (2004)
Dimitris Achlioptas, Cristopher Moore
Given any integer d 1, let k be the smallest integer such that d 2k log k. We prove that with high probability the chromatic number of a random d-regular graph is k, k + 1, or k + 2.
Random Matrices in Data Analysis (2004)
We show how carefully crafted random matrices can achieve distance-preserving dimensionality reduction, accelerate spectral computations, and reduce the sample complexity of certain kernel methods.
Hiding Satisfying Assignments: Two are Better than One (2004)
Dimitris Achlioptas, Haixia Jia, Cristopher Moore
The evaluation of incomplete satisfiability solvers depends critically on the availability of hard satisfiable instances. A plausible source of such instances consists of random k-SAT formulas whose...
Exponential bounds for DPLL below the satisfiability threshold (2004)
Dimitris Achlioptas, Paul Beame, Michael Molloy
Abstract For each k * 4, we give rk? 0 such that a random k-CNF formula F with n variables and brknc clauses is satisfiable with high probability, but ordered-dll takes exponential time on F with...
Hiding satisfying assignments: two are better than one (2004)
Dimitris Achlioptas, Haixia Jia
The evaluation of incomplete satisfiability solvers depends critically on the availability of hard satisfiable instances. A plausible source of such instances consists of random k-SAT formulas whose...
Exponential bounds for DPLL below the satisfiability threshold (2004)
Dimitris Achlioptas, Paul Beame, Michael Molloy
Abstract For each k> = 4, we give rk> 0 such that a random k-CNF formula F with n variables and brknc clausesis satisfiable with high probability, but ordered-dlltakes exponential time on F...
Hiding satisfying assignments: two are better than one (2004)
Dimitris Achlioptas, Haixia Jia
The evaluation of incomplete satisfiability solvers depends critically on the availability of hard satisfiable instances. A plausible source of such instances consists of random k-SAT formulas whose...
Random matrices in data analysis (2004)
Abstract. We show how carefully crafted random matrices can achieve distance-preserving dimensionality reduction, accelerate spectral computations, and reduce the sample complexity of certain kernel...
The chromatic number of random regular graphs (2004)
Dimitris Achlioptas, Cristopher Moore
Abstract. Given any integer d ≥ 3, let k be the smallest integer such that d<2k log k. We prove that with high probability the chromatic number of a random d-regular graph is k, k +1,ork +2. 1
Exponential bounds for DPLL below the satisfiability threshold (2004)
Dimitris Achlioptas, Paul Beame, Michael Molloy
For each k ≥ 4, we give rk> 0 such that a random k-CNF formula F with n variables and ⌊rkn ⌋ clauses is satisfiable with high probability, but ordered-dll takes exponential time on F with...
Frank Mcsherry, Frank Mcsherry, Anna Karlin, Dimitris Achlioptas, Paul Beame, Anna Karlin, ...
Reading Committee: Date: and that any and all revisions required by the final examining committee have been made.
Random k-SAT: Two Moments Suffice to Cross a Sharp Threshold (2003)
Achlioptas, Dimitris, Moore, Cristopher
Many NP-complete constraint satisfaction problems appear to undergo a "phase transition'' from solubility to insolubility when the constraint density passes through a critical threshold. In all such...
The Threshold for Random k-SAT is 2^k ln2 - O(k) (2003)
Achlioptas, Dimitris, Peres, Yuval
Let F be a random k-SAT formula on n variables, formed by selecting uniformly and independently m = rn out of all possible k-clauses. It is well-known that if r>2^k ln 2, then the formula F is...
On the Maximum Satisfiability of Random Formulas (2003)
Achlioptas, Dimitris, Naor, Assaf, Peres, Yuval
Maximum satisfiability is a canonical NP-hard optimization problem that appears empirically hard for random instances. Let us say that a Conjunctive normal form (CNF) formula consisting of...
Sampling grid colourings with fewer colours (2003)
Dimitris Achlioptas, Mike Molloy, Cristopher Moore, Frank Van Bussel
We provide an optimally mixing Markov chain for 6-colourings of the square grid. Furthermore, this implies that the uniform distribution on the set of such colourings has strong spatial mixing. 4 and...
On the Fraction of Satisfiable Clauses in Typical Formulas (2003)
Dimitris Achlioptas, Assaf Naor, Yuval Peres
Given n Boolean variables x1,..., xn, a k-clause is a disjunction of k literals, where a literal is a variable or its negation. A k-CNF formula is a conjunction of a finite number of k-clauses. Call...
On the maximum satisfiability of random formulas (2003)
Dimitris Achlioptas, Assaf Naor, Yuval Peres
Say that a k-CNF a formula is p-satisfiable if there exists a truth assignment satisfying a fraction 1 − 2 −k + p2 −k of its clauses (note that every k-CNF formula is 0-satisfiable). Let Fk(n,...
The Asymptotic Order of the k-SAT Threshold (2002)
Achlioptas, Dimitris, Moore, Cristopher
Form a random k-SAT formula on n variables by selecting uniformly and independently m=rn clauses out of all 2^k (n choose k) possible k-clauses. The Satisfiability Threshold Conjecture asserts that...
The Asymptotic Order of the Random k-SAT Threshold (2002)
Form a random k-SAT formula on n variables by selecting uniformly and independently m = rn clauses out of all 2 k n
On the 2-colorability of Random Hypergraphs (2002)
Dimitris Achlioptas, Cristopher Moore
Abstract. A 2-coloring of a hypergraph is a mapping from its vertices to a set of two colors such that no edge is monochromatic. Let Hk (n; m) be a random k-uniform hypergraph on n vertices formed by...
Almost all graphs with average degree 4 are 3-colorable (2002)
Dimitris Achlioptas, Cristopher Moore
We analyze a randomized version of the Brelaz heuristic on sparse random graphs. We prove that almost all graphs with average degree d 4.03, i.e. G(n, p = d/n), are 3-colorable and that a constant...
Sampling techniques for kernel methods (2002)
Dimitris Achlioptas, Frank Mcsherry, Bernhard Sch Olkopf
We propose randomized techniques for speeding up Kernel Principal Component Analysis on three levels: sampling and quantization of the Gram matrix in training, randomized rounding in evaluating the...
Two-coloring random hypergraphs (2002)
Dimitris Achlioptas, Jeong Han Kim, Michael Krivelevich
A 2-coloring of a hypergraph is a mapping from its vertex set to a set of two colors such that no edge is monochromatic. Let H = H(k;n; p) be a random k-uniform hypergraph on a vertex set V of...
Sampling techniques for kernel methods (2002)
Dimitris Achlioptas, Frank Mcsherry, Bernhard Sch Olkopf
We propose randomized techniques for speeding up Kernel Principal Component Analysis on three levels: sampling and quantization of the Gram matrix in training, randomized rounding in evaluating the...
Sampling techniques for kernel methods (2002)
Correspondence Frank Mcsherry, Dimitris Achlioptas, Frank Mcsherry, Bernhard Sch Olkopf
We propose sampling methods for speeding up kernel techniques on three levels. We sparsify the Gram matrix, the kernel expansion, and, for a class of commonly used kernels, we propose a sampling...
Two-coloring Random Hypergraphs (2002)
Dimitris Achlioptas, Jeong Han Kim, Michael Krivelevich, Prasad Tetali
A 2-coloring of a hypergraph is a mapping from its vertex set to a set of two colors such that no edge is monochromatic. Let H = H(k;n; p) be a random k-uniform hypergraph on a vertex set V of...
Almost All Graphs With Average Degree 4 Are 3-Colorable (2002)
Dimitris Achlioptas Microsoft, Dimitris Achlioptas
The technique of using di#erential equations to approximate the mean path of Markov chains has proved very useful in the average-case analysis of algorithms. Here, we significantly expand the range...
Two-coloring random hypergraphs (2002)
Dimitris Achlioptas, Jeong Han Kim, Michael Krivelevich, Prasad Tetali
ABSTRACT: A 2-coloring of a hypergraph is a mapping from its vertex set to a set of two colors such that no edge is monochromatic. Let H = H�k � n � p � be a random k-uniform hypergraph on a...
On the 2-colorability of Random Hypergraphs (2002)
Dimitris Achlioptas, Cristopher Moore
Abstract. A2-coloring of a hypergraph is a mapping from its vertices to a set of two colors such that no edge is monochromatic. Let Hk(n, m) be a random k-uniform hypergraph on n vertices formed by...
Almost all graphs with average degree 4 are 3-colorable (2002)
Dimitris Achlioptas, Cristopher Moore
The technique of approximating the mean path of Markov chains by differential equations has proved to be a useful tool in analyzing the performance of heuristics on random graph instances. However,...
the World Wide Web. comment, Science, 287:2115a, 2000. (2001)
Webgraph Papers, Daniel M. Abrams, Dimitris Achlioptas, Amos Fiat, Anna R. Karlin, Frank Mcsherry, ...
In Proceedings of the thirty-second annual ACM symposium on Theory of computing, pages 171–180, 2000. [12] William Aiello, Fan R. K. Chung, and Linyuan Lu. Random evolution
Lower bounds for random 3-SAT via dierential equations (2001)
www.elsevier.com/locate/tcs
The phase transition in 1-in-k SAT and NAE 3-SAT (2001)
Dimitris Achlioptas, Arthur Chtcherba, Gabriel Istrate, Cristopher Moore
Determining bounds for the random k-SAT threshold has been an active area of research in recent years [1, 3]. Yet, in spite of signicant eorts,
A sharp threshold in proof complexity (2001)
Dimitris Achlioptas, Paul Beame, Michael Molloy
We give the rst example of a sharp threshold in proof complexity. More precisely, we show that for any > 0 and > 2:28, random formulas consisting of (1 )n 2clauses and n 3-clauses, which are...
A sharp threshold in proof complexity (2001)
Dimitris Achlioptas, Paul Beame, Michael Molloy
We give the first example of a sharp threshold in proof complexity. More precisely, we show that for any sufficiently small > 0 and > 2:28, random formulas consisting of (1 )n 2-clauses and n...
Fast computation of low rank matrix approximations (2001)
Given a matrix A it is often desirable to nd an approximation to A that has low rank. We introduce a simple technique for accelerating the computation of such approximations when A has strong...
Balance and filtering in structured satisfiable problems (2001)
Yongshao Ruan, Dimitris Achlioptas
New methods to generate hard random problem instances have driven progress on algorithms for deduction and constraint satisfaction. Recently Achlioptas et al. (AAAI 2000) introduced a new generator...
Database-friendly random projections (2001)
A classic result of Johnson and Lindenstrauss asserts that any set of n points in d-dimensional Euclidean space can be embedded into k-dimensional Euclidean space | where k is logarithmic in n and...
The phase transition in 1-in-k SAT and NAE 3-SAT (2001)
Dimitris Achlioptas, Arthur Chtcherba, Gabriel Istrate, Cristopher Moore
Determining bounds for the random k-SAT thresh-old has been an active area of research in recent years [1, 3]. Yet, in spite of significant efforts, nei-ther a tight analysis nor the structural...
Web search via hub synthesis (2001)
Dimitris Achlioptas, Amos Fiatý, Anna R. Karlinþ, Frank Mcsherryü
Small have continual plodders ever won save base authority from others books. — William Shakespeare, Loves Labours Lost. Act i. Sc. 1. They define themselves in terms of what they oppose. —...
A classic result of Johnson and Lindenstrauss asserts that any set of n points in d-dimensional Euclidean space can be embedded into k-dimensional Euclidean space—where k is logarithmic in n and...
Web search via hub synthesis (2001)
Dimitris Achlioptas, Amos Fiat, Anna R. Karlin, Frank Mcsherry
Small have continual plodders ever won save base authority from others books. — William Shakespeare, Loves Labours Lost. Act i. Sc. 1. They define themselves in terms of what they oppose. —...
Database-friendly random projections (2001)
A classic result of Johnson and Lindenstrauss asserts that any set of Ò points in �-dimensional Euclidean space can be embedded into �-dimensional Euclidean space — where � is logarithmic in...
A sharp threshold in proof complexity (2001)
Dimitris Achlioptas, Paul Beame, Michael Molloy
We give the first example of a sharp threshold in proof complexity. More precisely, we show that for any sufficiently small � and � � �, random formulas consisting of 2-clauses and 3-clauses,...
Optimal myopic algorithms for random 3-SAT (2000)
Dimitris Achlioptas, Gregory B. Sorkin
Let F 3 (n; m) be a random 3-SAT formula formed by selecting uniformly, independently, and with replacement, m clauses among all 8
Generating Satisfiable Problem Instances (2000)
Dimitris Achlioptas, Henry Kautz, Carla Gomes
A major difficulty in evaluating incomplete local search style algorithms for constraint satisfaction problems is the need for a source of hard problem instances that are guaranteed to be...
Generating Satisfiable Problem Instances (2000)
Dimitris Achlioptas Microsoft, Dimitris Achlioptas, Carla Gomes, Henry Kautz, Bart Selman
A major difficulty in evaluating incomplete local search style algorithms for constraint satisfaction problems is the need for a source of hard problem instances that are guaranteed to be...
Optimal myopic algorithms for random 3-SAT (2000)
Dimitris Achlioptas, Gregory B. Sorkin
Let F3(n, m) be a random 3-SAT formula formed by selecting uniformly, independently, and with replacement, m clauses among all 8 (y) possible 3-clauses over n vari-ables. It has been conjectured that...
Tight lower bounds for st-connectivity on the NNJAG model (1999)
Jeff Edmonds, Chung Keung Poon, Dimitris Achlioptas
Abstract. Directed st-connectivity is the problem of deciding whether or not there exists a path from a distinguished node s to a distinguished node t in a directed graph. We prove a time– space...
Abstract Threshold Phenomena in Random Graph Colouring and Satisfiability (1999)
Dimitris Achlioptas, Dimitris Achlioptas, Dimitris Achlioptas
We study threshold phenomena pertaining to the colourability of random graphs and the satisfiability of random formulas. Consider a random graph G(n, p) on n vertices formed by including each of the
A sharp threshold for k-colorability (1999)
Dimitris Achlioptas, Ehud Friedgut
Let k be a fixed integer and f k (n; p) denote the probability that the random graph G(n; p) is k-colorable. We show that for every k 3, there exists d k (n) such that for any ffl? 0, lim n!1 f k (n;...
Almost all graphs with 2.522n edges are not 3-colorable (1999)
Dimitris Achlioptas, Michael Molloy
We prove that for c 2:522 a random graph with n vertices and m = cn edges is not 3-colorable with probability 1 o(1). Similar bounds for non-k-colorability are given for k> 3. 1991 Mathematics...
Almost all graphs with 2.522n edges are not 3-colorable (1999)
Dimitris Achlioptas, Michael Molloy
We show that if a random graph on n vertices has m = (r + o(1))n edges, where r=2.522, then almost surely it is not 3-colorable. The previous best such value for r was 2.571[5]. Our result follows...
Almost All Graphs with 2.522n Edges Are Not 3-Colorable (1999)
Dimitris Achlioptas, Michael Molloy
We prove that for c # 2.522 a random graph with n vertices and m = cn edges is not 3-colorable with probability 1 - o(1). Similar bounds for non-k-colorability are given for k>3. 1991 Mathematics...
Setting 2 variables at a time yields a new lower bound for random 3-SAT (Extended Abstract) (1999)
Let X be a set of n Boolean variables and denote by C(X) the set of all 3-clauses over X, i.e. the set of all 8 n 3 possible disjunctions of three distinct, non-complementary literals from variables...
Setting 2 variables at a time yields a new lower bound for random 3-SAT (1999)
Dimitris Achlioptas, Dimitris Achlioptas
Let X be a set of n Boolean variables and denote by C(X) be the set of all 3-clauses over X , i.e. the set of all 8 n 3 possible disjunctions of three distinct, non-complementary literals of...
Almost All Graphs With 2.522n Edges Are Not 3-Colorable (1999)
Dimitris Achlioptas, Michael Molloy
We prove that for c 2:522 a random graph with n vertices and m = cn edges is not 3-colorable with probability 1 \Gamma o(1). Similar bounds for non-k-colorability are given for k ? 3. 1991...
Almost All Graphs With 2.522n Edges Are Not 3-Colorable (1999)
Dimitris Achlioptas, Michael Molloy
We show that a random graph on n vertices with m = rn edges is almost surely not 3-colorable, if r 2:522. This follows from a refinement of the first moment argument for almost sure...
Tight Lower Bounds for st-Connectivity on the NNJAG Model (1999)
Jeff Edmonds, Chung Keung Poon, Dimitris Achlioptas, Otherwise T \omega\gamma
Directed st-connectivity is the problem of deciding whether or not there exists a path from a distinguished node s to a distinguished node t in a directed graph. We prove a time-space lower bound on...
Tight Lower Bounds For st-Connectivity On The NNJAG Model (1999)
Jeff Edmonds, Chung Keung Poon, Dimitris Achlioptas, Society For Industrial
Directed st-connectivity is the problem of deciding whether or not there exists a path from a distinguished node s to a distinguished node t in a directed graph. We prove a time-space lower bound on...
St-Connectivity On, Jeff Edmonds, Chung Keung Poon, Dimitris Achlioptas, Otherwise T \omega\gamma
Directed st-connectivity is the problem of deciding whether or not there exists a path from a distinguished node s to a distinguished node t in a directed graph. We prove a time-space lower bound on...
Random Constraint Satisfaction: A More Accurate Picture (1998)
Dimitris Achlioptas, Lefteris M. Kirousis, Evangelos Kranakis, Danny Krizanc, Yannis C. Stamatiou
In the last few years there has been a great amount of interest in Random Constraint Satisfaction Problems, both from an experimental and a theoretical point of view. Quite intriguingly, experimental...
Dimitris Achlioptas, Ehud Friedgut
ABSTRACT: Let k be a fixed integer and f Ž n, p. k denote the probability that the random graph Gn, Ž p. is k-colorable. We show that for k�3, there exists d Ž n. k such that for any ��0, ž...
Rigorous Results for Random (2+p)-SAT (1997)
Dimitris Achlioptas, Lefteris M. Kirousis, Evangelos Kranakis, Danny Krizanc
zk
The analysis of a list-coloring algorithm on a random graph (1997)
Dimitris Achlioptas, Michael Molloy
We introduce a natural k-coloring algorithm and analyze its performance on random graphs with constant expected degree c (G n;p=c=n). For k = 3 our results imply that almost all graphs with n...
Random constraint satisfaction: A more accurate picture (1997)
Dimitris Achlioptas, Lefteris M. Kirousis, Evangelos Kranakis, Danny Krizanc, Yannis C. Stamatiou
zk
Random constraint satisfaction: A more accurate picture (1997)
Dimitris Achlioptas, Lefteris M. Kirousis, Evangelos Kranakis, Danny Krizanc, Yannis C. Stamatiou
y--
Random Constraint Satisfaction: A More Accurate Picture (1997)
Dimitris Achlioptas, Lefteris M. Kirousis, Evangelos Kranakis, Danny Krizanc, Yannis C. Stamatiou
. In the last few years there has been a great amount of interest in Random Constraint Satisfaction Problems, both from an experimental and a theoretical point of view. Quite intriguingly,...
The Analysis of a List-Coloring Algorithm on a Random Graph (Extended Abstract) (1997)
Dimitris Achlioptas, Michael Molloy
We introduce a natural k-coloring algorithm and analyze its performance on random graphs with constant expected degree c (G n;p=c=n ). For k = 3 our results imply that almost all graphs with n...
A Sharp Threshold for k-Colorability (1997)
Dimitris Achlioptas, Ehud Friedgut
Let k be a xed integer and f k (n; p) denote the probability that the random graph G(n; p) is k-colorable. We show that for k 3, there exists d k (n) such that for any > 0, lim n!1 f k (n; d k (n)...
Random Constraint Satisfaction: A More Accurate Picture (1997)
Dimitris Achlioptas, Lefteris M. Kirousis, Evangelos Kranakis, Danny Krizanc, Yannis C. Stamatiou
. In the last few years there has been a great amount of interest in Random Constraint Satisfaction Problems, both from an experimental and a theoretical point of view. Quite intriguingly,...
Rigorous Results for Random (2+p)-SAT (1997)
Dimitris Achlioptas, Lefteris M. Kirousis, Evangelos Kranakis, Danny Krizanc
Consider random k-SAT instances with rn clauses over n variables, where each clause is chosen uniformly and independently from the set of all clauses of length k. It is widely believed that for all k...
Random Constraint Satisfaction: A More Accurate Picture (1997)
Dimitris Achlioptas, Lefteris M. Kirousis, Evangelos Kranakis, Danny Krizanc, Yannis C. Stamatiou
Recently there has been a great amount of interest in Random Constraint Satisfaction Problems, both from an experimental and a theoretical point of view. Rather intriguingly, experimental results...
A Sharp Threshold for k-Colorability (1997)
Dimitris Achlioptas, Ehud Friedgut
Let f k (n; p) denote the probability that the random graph G(n; p) is k-colorable. We show that for every k 3, there exists d k (n) such that for any ffl ? 0, lim n!1 f k (n; d k (n) \Gamma ffl n )...
Random Constraint Satisfaction: A More Accurate Picture (1997)
Dimitris Achlioptas, Lefteris M. Kirousis, Evangelos Kranakis, Danny Krizanc, Michael S.O., ...
Recently there has been a great amount of interest in Random Constraint Satisfaction Problems, both from an experimental and a theoretical point of view. Rather intriguingly, experimental results...
Random constraint satisfaction: A more accurate picture (1997)
Dimitris Achlioptas, Lefteris M. Kirousis, Evangelos Kranakis, Danny Krizanc, Yannis C. Stamatioux
Random constraint satisfaction: A more accurate picture (1997)
Abstract. In the last few years there has been a great amount of interest in Random Constraint Satisfaction Problems, both from an experimental and a theoretical point of view. Quite intriguingly,...
Competitive Analysis of Randomized Paging Algorithms (1996)
Dimitris Achlioptas, Marek Chrobak, John Noga, Communicated F. Yao
The paging problem is de#ned as follows: we are given a two-level memory system, in which one level is a fast memory, called cache, capable of holding k items, and the second level is an unbounded...
A Correlation Inequality and Its Application to a Word Problem (1996)
Dimitris Achlioptas, Lefteris M. Kirousis, Evangelos Kranakis, Danny Krizanc, Michael S. Molloy
We give upper bounds for the probability that a random word of a given length contains at least one letter from each member of a given collection of sets of letters. We first show a correlation...
Competitive Analysis of Randomized Paging Algorithms (1996)
Dimitris Achlioptas, Marek Chrobak, John Noga
The paging problem is defined as follows: we are given a two-level memory system, in which one level is a fast memory, called cache, capable of holding k items, and the second level is an unbounded...
Competitive Analysis of Randomized Paging Algorithms (1996)
Dimitris Achlioptas, Marek Chrobak, John Noga
The paging problem is defined as follows: we are given a two-level memory system, in which one level is a fast memory, called cache, capable of holding k items, and the second level is an unbounded...
Almost All Graphs of Degree 4 are 3-colorable
Dimitris Achlioptas, Cristopher Moore
The technique of approximating the mean path of Markov chains by differential equations has proved to be a useful tool in analyzing the performance of heuristics on random graph instances. However,...
The Two Possible Values of the Chromatic Number of a Random Graph
Dimitris Achlioptas, Assaf Naor
Given d let k d be the smallest integer k such that d < 2k log k. We prove that the chromatic number of a random graph G(n, d/n) is either k d or k d + 1 almost surely. 1