47 Hits in 1.4 sec

Counting connected graphs with large excess [article]

Elie de Panafieu
2016 arXiv   pre-print
Exact and asymptotic results on connected multigraphs are available in de Panafieu (2014).  ...  The proofs rely on tools developed by de Panafieu and Ramos (2016) ; Collet et al. (2016) . Theorem 2.  ... 
arXiv:1604.07307v1 fatcat:zyhhzbfkknddbp6kxmsb5ejxiq

Graphs with degree constraints [article]

Élie de Panafieu, Lander Ramos
2015 arXiv   pre-print
In de Panafieu (2014), following the same approach, but using analytic combinatorics, we obtained a short proof for the asymptotics of connected multigraphs from MG n,m when m − n tends to infinity.  ... 
arXiv:1506.03061v2 fatcat:47gokujgl5f4vmcqi5esscgaym

Active clustering for labeling training data [article]

Quentin Lutz, Élie de Panafieu, Alex Scott, Maya Stein
2021 arXiv   pre-print
Quentin Lutz and Élie de Panafieu produced part of this work at Lincs ( Quentin Lutz is supported by Nokia Bell Labs (CIFRE convention 2018/1648).  ... 
arXiv:2110.14521v1 fatcat:xhg2qnnp6nempm6d6dmpgtvkdy

Analytic Description of the Phase Transition of Inhomogeneous Multigraphs [article]

Élie de Panafieu, Vlady Ravelomanana
2014 arXiv   pre-print
We introduce a new model of random multigraphs with colored vertices and weighted edges. It is similar to the "inhomogeneous random graph model" of S\"oderberg (2002), extended by Bollob\'as, Janson and Riordan (2007). By means of analytic combinatorics, we then analyze the birth of "complex components", which are components with at least two cycles. We apply those results to give a complete picture of the finite size scaling and the critical exponents associated to a rather broad family of
more » ... sion problems. As applications, we derive new proofs of known results on the 2-colorability problem, already investigated by Pittel and Yeum (2010), and on the enumeration of properly q-colored multigraphs, analyzed by Wright (1972). We also obtain new results on the phase transition of the satisfiability of quantified 2-Xor-formulas, a problem introduced by Creignou, Daud\'e and Egly (2007).
arXiv:1409.8424v1 fatcat:j27y5y5eg5bitf5rj4x3fkf5su

Enumeration and structure of inhomogeneous graphs [article]

Élie de Panafieu
2015 arXiv   pre-print
We analyze a general model of weighted graphs, introduced by de Panafieu and Ravelomanana (2014) and similar to the "inhomogeneous graph model" of Söderberg (2002).  ...  We consider in this paper a variant of this model, introduced by de Panafieu and Ravelomanana (2014) and closer to the uniform graph model.  ...  In this article, we focus on a model of inhomogeneous graphs introduced by de Panafieu and Ravelomanana (2014) and similar to the inhomogeneous graph model of Söderberg (2002) .  ... 
arXiv:1501.07775v2 fatcat:h77ehaleg5hshdvq47zozpl5oe

Exact enumeration of satisfiable 2-SAT formulae [article]

Sergey Dovgal and Élie de Panafieu and Vlady Ravelomanana
2021 arXiv   pre-print
.: ANR-18-CE25-0002.Élie de Panafieu was supported by the Lincs ( and the Rise project RandNET, grant no.: H2020-EU.1.3.3.  ... 
arXiv:2108.08067v1 fatcat:kxuoquwxz5gobldqg3zw5rtehy

Symbolic method and directed graph enumeration [article]

Élie de Panafieu, Sergey Dovgal
2019 arXiv   pre-print
We introduce the arrow product, a systematic generating function technique for directed graph enumeration. It provides short proofs for previous results of Gessel on the number of directed acyclic graphs and of Liskovets, Robinson and Wright on the number of strongly connected directed graphs. We also recover Robinson's enumerative results on directed graphs where all strongly connected components belong to a given family.
arXiv:1903.09454v2 fatcat:t5ouk2e5trf4zpnaa4skn2bsum

Limit Distribution of Two Skellam Distributions, Conditionally on Their Equality [article]

François Durand, Élie de Panafieu
2021 arXiv   pre-print
Consider two random variables following Skellam distributions of parameters going to infinity linearly. We prove that the limit distribution of the first variable, conditionally on being equal to the second, is Gaussian.
arXiv:2102.10835v1 fatcat:o7kxfq5k3jb6jdw5koll2admje

Counting directed acyclic and elementary digraphs [article]

Élie de Panafieu, Sergey Dovgal
2020 arXiv   pre-print
Directed acyclic graphs (DAGs) can be characterised as directed graphs whose strongly connected components are isolated vertices. Using this restriction on the strong components, we discover that when m = cn, where m is the number of directed edges, n is the number of vertices, and c < 1, the asymptotic probability that a random digraph is acyclic is an explicit function p(c), such that p(0) = 1 and p(1) = 0. When m = n(1 + μ n^-1/3), the asymptotic behaviour changes, and the probability that a
more » ... digraph is acyclic becomes n^-1/3 C(μ), where C(μ) is an explicit function of μ. Łuczak and Seierstad (2009, Random Structures Algorithms, 35(3), 271–293) showed that, as μ→ -∞, the strongly connected components of a random digraph with n vertices and m = n(1 + μ n^-1/3) directed edges are, with high probability, only isolated vertices and cycles. We call such digraphs elementary digraphs. We express the probability that a random digraph is elementary as a function of μ. Those results are obtained using techniques from analytic combinatorics, developed in particular to study random graphs.
arXiv:2001.08659v2 fatcat:xub7jlxcvzf3vmbxajle7cgn3y

Phase Transition of Random Non-uniform Hypergraphs [chapter]

Élie de Panafieu
2013 Lecture Notes in Computer Science  
The authors use them to give a combinatorial interpretation of a functional equation of Bouwkamp and de Bruijn.  ...  However, similar generating functions have been derived in [11] for a different purpose: Gessel and Kalikow use it to give a combinatorial interpretation for a functional equation of Bouwkamp and de  ... 
doi:10.1007/978-3-642-45278-9_12 fatcat:r346m5owafhrtoo45oepwpjo4a

Analytic combinatorics of connected graphs [article]

Elie de Panafieu
2018 arXiv   pre-print
graphs (de Panafieu (2015a) ; de Panafieu and Ravelomanana (2015) ).  ...  We are currently working on the structure of random graphs with degree constraints (to extend the work of de Panafieu and Ramos (2016)), of non-uniform hypergraphs (de Panafieu (2015b) ), and of inhomogeneous  ... 
arXiv:1605.08597v3 fatcat:avhdgh3wcnfdxbxgqx5jnyh7pm

Of Kernels and Queues: when network calculus meets analytic combinatorics [article]

Anne Bouillard, Céline Comte, Élie De Panafieu, Fabien Mathieu
2018 arXiv   pre-print
Stochastic network calculus is a tool for computing error bounds on the performance of queueing systems. However, deriving accurate bounds for networks consisting of several queues or subject to non-independent traffic inputs is challenging. In this paper, we investigate the relevance of the tools from analytic combinatorics, especially the kernel method, to tackle this problem. Applying the kernel method allows us to compute the generating functions of the queue state distributions in the
more » ... onary regime of the network. As a consequence, error bounds with an arbitrary precision can be computed. In this preliminary work, we focus on simple examples which are representative of the difficulties that the kernel method allows us to overcome.
arXiv:1810.04875v1 fatcat:a6thwd3rtvaxfobsdqcvky2gqi

Threshold functions for small subgraphs: an analytic approach [article]

Gwendal Collet, Élie de Panafieu, Danièle Gardy, Bernhard Gittenberger, Vlady Ravelomanana
2017 arXiv   pre-print
We revisit the problem of counting the number of copies of a fixed graph in a random graph or multigraph, including the case of constrained degrees. Our approach relies heavily on analytic combinatorics and on the notion of patchwork to describe the possible overlapping of copies. This paper is a version, extended to include proofs, of the paper with the same title to be presented at the Eurocomb 2017 meeting.
arXiv:1705.08768v1 fatcat:wwwwa4zy5zer7jvfuj46ah44p4

2-Xor revisited: satisfiability and probabilities of functions [article]

Élie de Panafieu and Danièle Gardy and Bernhard Gittenberger and Markus Kuba
2015 arXiv   pre-print
The problem 2-Xor-Sat asks for the probability that a random expression, built as a conjunction of clauses x ⊕ y, is satisfiable. We revisit this classical problem by giving an alternative, explicit expression of this probability. We then consider a refinement of it, namely the probability that a random expression computes a specific Boolean function. The answers to both problems involve a description of 2-Xor expressions as multigraphs and use classical methods of analytic combinatorics by
more » ... essing probabilities through coefficients of generating functions.
arXiv:1511.07813v1 fatcat:dqhrrs7cibdr5kkkxuilljrmr4

Counting connected graphs with large excess

Élie De Panafieu
2020 Discrete Mathematics & Theoretical Computer Science  
Exact and asymptotic results on connected multigraphs are available in de Panafieu (2014).  ...  The proofs rely on tools developed by de Panafieu and Ramos (2016) ; Collet et al. (2016) .  ... 
doi:10.46298/dmtcs.6368 fatcat:tng4iqeklzffpfq773s5civbjq
« Previous Showing results 1 — 15 out of 47 results