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Laurent Bulteau

Publications and source records attributed to Laurent Bulteau.

27 records · Page 2Linked to original sources
arXiv2016

Decomposing Cubic Graphs into Connected Subgraphs of Size Three

Let $S=\{K_{1,3},K_3,P_4\}$ be the set of connected graphs of size 3. We study the problem of partitioning the edge set of a graph $G$ into graphs taken from any non-empty $S'\subseteq S$. The problem is known to be NP-complete for any possible choice of $S'$ in general graphs. In this paper, we assume that the input graph is cubic, and study the computational complexity of the problem of partitioning its edge set for any choice of $S'$. We identify all polynomial and NP-complete problems in that setting, and give graph-theoretic characterisations of $S'$-decomposable cubic graphs in some cases.

cs.DS↗
arXiv2015

The Complexity of Finding Effectors

The NP-hard EFFECTORS problem on directed graphs is motivated by applications in network mining, particularly concerning the analysis of probabilistic information-propagation processes in social networks. In the corresponding model the arcs carry probabilities and there is a probabilistic diffusion process activating nodes by neighboring activated nodes with probabilities as specified by the arcs. The point is to explain a given network activation state as well as possible by using a minimum number of "effector nodes"; these are selected before the activation process starts. We correct, complement, and extend previous work from the data mining community by a more thorough computational complexity analysis of EFFECTORS, identifying both tractable and intractable cases. To this end, we also exploit a parameterization measuring the "degree of randomness" (the number of "really" probabilistic arcs) which might prove useful for analyzing other probabilistic network diffusion problems as well.

cs.DS↗
arXiv2015

Triangle counting in dynamic graph streams

Estimating the number of triangles in graph streams using a limited amount of memory has become a popular topic in the last decade. Different variations of the problem have been studied, depending on whether the graph edges are provided in an arbitrary order or as incidence lists. However, with a few exceptions, the algorithms have considered {\em insert-only} streams. We present a new algorithm estimating the number of triangles in {\em dynamic} graph streams where edges can be both inserted and deleted. We show that our algorithm achieves better time and space complexity than previous solutions for various graph classes, for example sparse graphs with a relatively small number of triangles. Also, for graphs with constant transitivity coefficient, a common situation in real graphs, this is the first algorithm achieving constant processing time per edge. The result is achieved by a novel approach combining sampling of vertex triples and sparsification of the input graph. In the course of the analysis of the algorithm we present a lower bound on the number of pairwise independent 2-paths in general graphs which might be of independent interest. At the end of the paper we discuss lower bounds on the space complexity of triangle counting algorithms that make no assumptions on the structure of the graph.

cs.DS↗
arXiv2014

Computing an Evolutionary Ordering is Hard

We prove that computing an evolutionary ordering of a family of sets, i.e. an ordering where each set intersects with --but is not included in-- the union earlier sets, is NP-hard.

cs.CC↗
arXiv2014

Combinatorial Voter Control in Elections

Voter control problems model situations such as an external agent trying to affect the result of an election by adding voters, for example by convincing some voters to vote who would otherwise not attend the election. Traditionally, voters are added one at a time, with the goal of making a distinguished alternative win by adding a minimum number of voters. In this paper, we initiate the study of combinatorial variants of control by adding voters: In our setting, when we choose to add a voter~$v$, we also have to add a whole bundle $κ(v)$ of voters associated with $v$. We study the computational complexity of this problem for two of the most basic voting rules, namely the Plurality rule and the Condorcet rule.

cs.MA↗
arXiv2013

A Fixed-Parameter Algorithm for Minimum Common String Partition with Few Duplications

Motivated by the study of genome rearrangements, the NP-hard Minimum Common String Partition problems asks, given two strings, to split both strings into an identical set of blocks. We consider an extension of this problem to unbalanced strings, so that some elements may not be covered by any block. We present an efficient fixed-parameter algorithm for the parameters number k of blocks and maximum occurrence d of a letter in either string. We then evaluate this algorithm on bacteria genomes and synthetic data.

cs.DS↗
arXiv2011

Pancake Flipping is Hard

Pancake Flipping is the problem of sorting a stack of pancakes of different sizes (that is, a permutation), when the only allowed operation is to insert a spatula anywhere in the stack and to flip the pancakes above it (that is, to perform a prefix reversal). In the burnt variant, one side of each pancake is marked as burnt, and it is required to finish with all pancakes having the burnt side down. Computing the optimal scenario for any stack of pancakes and determining the worst-case stack for any stack size have been challenges over more than three decades. Beyond being an intriguing combinatorial problem in itself, it also yields applications, e.g. in parallel computing and computational biology. In this paper, we show that the Pancake Flipping problem, in its original (unburnt) variant, is NP-hard, thus answering the long-standing question of its computational complexity.

cs.CC↗
arXiv2010

Sorting by Transpositions is Difficult

In comparative genomics, a transposition is an operation that exchanges two consecutive sequences of genes in a genome. The transposition distance, that is, the minimum number of transpositions needed to transform a genome into another, is, according to numerous studies, a relevant evolutionary distance. The problem of computing this distance when genomes are represented by permutations, called the Sorting by Transpositions problem, has been introduced by Bafna and Pevzner in 1995. It has naturally been the focus of a number of studies, but the computational complexity of this problem has remained undetermined for 15 years. In this paper, we answer this long-standing open question by proving that the Sorting by Transpositions problem is NP-hard. As a corollary of our result, we also prove that the following problem is NP-hard: given a permutation pi, is it possible to sort pi using db(pi)/3 permutations, where db(pi) is the number of breakpoints of pi?

cs.DS↗