Discrete Algorithms

Ces dernières années, l'anthropologie de l'État a évolué vers des perspectives nouvelles impliquant une critique des conceptions traditionnelles de l'État. Cette critique ne reprend pas la position de Radcliffe-Brown qui, on se souvient, caractérisait l'État comme « une illusion » (1940 : XXIII). Les études récentes concernant l'anthropologie de l'État n'acceptent pas non plus les approches communes à la philosophie et aux sciences politiques, où l'État figure comme un objet sui generis, avec toute la réification qu'implique l'identification d'une « institution ». Au lieu de poser comme objets l'appareil et l'idéologie étatiques, les recherches anthropologiques visent aujourd'hui à identifier « les processus étatiques », et l'enquête de terrain a souvent conduit les chercheurs à étudier ces processus tels qu'ils se donnent à voir au niveau local, où la population appréhende l'État à travers une série de restrictions et d'opportunités (Krohn-Hansen & Nustad, 2005 : 14). Ces enquêtes montrent que le domaine de l'État englobe des formes et des processus d'organisation très variés, tels les lois, les écoles, les routes, la fiscalité, qui renvoient à des processus étatiques dont les acteurs poursuivent des intérêts souvent contradictoires. Il s'agit ensuite d'analyser les images de l'État qui s'expriment dans les représentations et dans des registres de discours différents (Aretxaga

The high rate of dropout students in Indonesia remains a matter of considerable concern, as it erodes the quality of education and hinders the long-term development of human capital. The government of Indonesia has endeavored to address the issue of high dropout rates among students by implementing a range of initiatives. To demonstrate the effectiveness of this program, forecasting is necessary to measure and predict its outcomes. The purpose of this study is to utilize a time series approach, specifically the Autoregressive Integrated Moving Average (ARIMA) model, to predict the number of dropout students in the forthcoming years. This study employs a quantitative analysis using secondary data obtained from Statistics Indonesia (BPS) for the period 1970-2023. The ARIMA method is a statistical technique used to determine the most suitable forecasting model from historical data. This method has gained widespread popularity in the field of time series analysis due to its ability to manage non-stationary data effectively. The result shows that ARIMA (0,2,1) has the smallest AIC and meets the significant criteria model, also having the lowest MAPE value of 1.9%, indicating excellent forecasting accuracy. The plot of the result indicates a downward trend in the number of dropout students over the coming years. This downward trend aligns with the timeline of government interventions, suggesting a potential causal relationship between the implementation of educational support programs and the declining dropout rates. Thus, the prediction supports the effectiveness of these initiatives in mitigating dropout student in Indonesia.

This paper examines the activities of Martin Luther King Jr. through the lenses of strategic management and organizational leadership. Departing from traditional historical narratives, the article focuses on the managerial models that enabled the transformation of chaotic social protest into a highly structured political movement. Utilizing qualitative research and case study analysis (e.g., the Montgomery Bus Boycott and the organizational structure of the SCLC), this study demonstrates how King executed resource optimization, crisis management, and strategic communication discipline. The findings suggest that King's success was rooted in the synthesis of "transformational leadership" and pragmatic operational management. The research offers novel insights into social entrepreneurship and the logistics of non-violent resistance, providing significant relevance for contemporary management theories in a globalized context.

A lot of progress has been made in tiling theory in the last ten years after Thurston ([Thu90]), building on previous work by Conway and Lagarias ([CL90]), introduced height functions as a tool to encode and study tilings. This allowed the authors of this paper, in previous work ([Rém99], [Des01]), to prove that the set of lozenge (or domino) tilings of a holefree, general-shape domain in the plane can be endowed with a distributive lattice structure. In this paper, we see that this structure allows us in turn to construct an algorithm that is optimal with respect to both space and execution time to generate all the tilings of a domain D. We first recall some results about tilings and then we describe the algorithm.

A drawing of a graph is greedy if for each ordered pair of vertices u and v, there is a path from u to v such that the Euclidean distance to v decreases monotonically at every vertex of the path. From an application perspective, greedy drawings are especially relevant to support routing schemes in ad hoc wireless networks. The existence of greedy drawings has been widely studied under different topological and geometric constraints, such as planarity, face convexity, and drawing succinctness. We introduce greedy rectilinear drawings, where edges are horizontal or vertical segments. These drawings have several properties that improve human readability and support network routing. We address the problem of testing whether a planar rectilinear representation, i.e., a plane graph with prescribed vertex angles, admits a greedy rectilinear drawing. We give a characterization, a lineartime testing algorithm, and a full generative scheme for universal greedy rectilinear representations, i.e., those for which every drawing is greedy. For general greedy rectilinear representations, we give a combinatorial characterization and, based on it, a polynomial-time testing and drawing algorithm for a meaningful subset of instances.

We initiate the study of the following problem: Given a non-planar graph G and a planar subgraph S of G, does there exist a straight-line drawing Γ of G in the plane such that the edges of S are not crossed in Γ ? We give positive and negative results for different kinds of spanning subgraphs S of G. Moreover, in order to enlarge the subset of instances that admit a solution, we consider the possibility of bending the edges of G \ S; in this setting different trade-offs between number of bends and drawing area are given.

AbstractLet R be a set of red points and let B be a set of blue points. The point set P=R∪B is called equitable if ||B|−|R||⩽1 and it is called general if no two points are vertically or horizontally aligned. An orthogeodesic alternating path on P is a path such that each edge is an orthogeodesic chain connecting points of different color and such that no two edges cross. We consider the problem of deciding whether a set of red and blue points admits a Hamiltonian orthogeodesic alternating path, that is, an orthogeodesic alternating path visiting all points. We prove that every general equitable point set admits a Hamiltonian orthogeodesic alternating path and we present an O(nlog2n)-time algorithm for finding such a path, where n is the number of points. On the other hand, we show that the problem is NP-complete if the path must be on the grid (i.e., vertices and bends have integer coordinates). Further, we show that we can approximate the maximum length of an orthogeodesic alterna...

We address an open question of Francis and Steel about phylogenetic networks and trees. They give a polynomial time algorithm to decide if a phylogenetic network, N, is tree-based and pose the problem: given a fixed tree T and network N, is N based on T? We show that it is $$\textit{NP}$$NP-hard to decide, by reduction from 3-Dimensional Matching (3DM) and further that the problem is fixed-parameter tractable.

A graph F is called middle if there exists a graph G such that there is a one-to-one correspondence between the vertices of F and the vertices and edges of G such that two vertices of Fare adjacent if and only if the corresponding elements (considered as subsets of the set of vertices) have a non-empty intersection. In this paper we present a linear time algorithm for the recognition of the middle graphs. The algorithm is based on a computer-oriented characterization of middle graphs. We show also how the algorithm can be generalized to recognize the middle graphs of hypergraphs.

This paper introduces a new family of reconstruction codes which is motivated by applications in DNA data storage and sequencing. In such applications, DNA strands are sequenced by reading some subset of their substrings. While previous works considered two extreme cases in which all substrings of predefined lengths are read or substrings are read with no overlap for the single string case, this work studies two extensions of this paradigm. The first extension considers the setup in which consecutive substrings are read with some given minimum overlap. First, an upper bound is provided on the attainable rates of codes that guarantee unique reconstruction. Then, efficient constructions of codes that asymptotically meet that upper bound are presented. In the second extension, we study the setup where multiple strings are reconstructed together. Given the number of strings and their length, we first derive a lower bound on the read substrings' length ℓ that is necessary for the existence of multi-strand reconstruction codes with non-vanishing rates. We then present two constructions of such codes and show that their rates approach 1 for values of ℓ that asymptotically behave like the lower bound.

Next-generation sequencing technologies have redefined the way genome sequencing is performed. They are able to produce tens of millions of short sequences (reads), during a single experiment, and with a much lower cost than previously possible. Due to the dramatic increase in the amount of data generated, a challenging task is to map (align) a set of reads to a reference genome. In this paper, we study a different version of this problem: mapping these reads to a dynamically changing genomic sequence. We propose a new practical algorithm, which employs a suitable data structure that takes into account potential dynamic effects (replacements, insertions, deletions) on the genomic sequence. The presented experimental results demonstrate that the proposed approach can be extended and applied to address the problem of mapping short reads to multiple related genomes.

The Parikh matrix of a word $w$ over an alphabet $\{a_1, \cdots , a_k \}$ with an ordering $a_1 < a_2 < \cdots a_k,$ gives the number of occurrences of each factor of the word $a_1 \cdots a_k$ as a (scattered) subword of the word $w.$ Two words $u,v$ are said to be $M-$equivalent, if the Parikh matrices of $u$ and $v$ are the same. On the other hand properties of image words under different morphisms have been studied in the context of subwords and Parikh matrices. Here an extension to three letters, introduced by S$\acute{e}\acute{e}$bold (2003), of the well-known Thue morphism on two letters, is considered and properties of Parikh matrices of morphic images of words are investigated. The significance of the contribution is that various classes of binary words are obtained whose images are $M-$equivalent under this extended morphism.

Nous tenons à remercier l'ensemble des clients, vendeuses et producteurs de fleurs coupées de la région d'Iquitos, en particulier ceux de Lupuna II Zona, qui ont accueilli avec curiosité nos questions. Nos assistants de recherche, Roxana Nascimiento et Carlos Rengifo Upiachihua, nous ont apporté une aide précieuse tout le long de ces recherches. Cette étude a été possible grâce à l'aide financière du Département de géographie de l'université McGill (Montréal, Canada) et du Conseil de recherches en sciences humaines (CRSH). Enfin, nous tenons à remercier Ludivine Eloy pour sa relecture et ses commentaires éclairés sur ce texte. 1 Pour les articles les plus récents, voir Hughes (2001) ; Newman (2002) ; Loges et al (2005) ; Baris & Uslu (2009) ; Muhammad et al (2009) ; Riisgaard (2009 & 2011) ; Mano et al (2011).

Given a graph G, a k-total difference labeling of the graph is a total labeling f from the set of edges and vertices to the set {1, 2, • • • k} satisfying that for any edge {u, v}, f is the minimum k such that there is a k-total difference labeling of G in which no two adjacent labels are identical. We extend prior work on total difference labeling by improving the upper bound on χ td (Kn) and also by proving results concerning infinite regular graphs. By a k-vertex labeling of a graph, we mean a function f from the vertices to the positive integers {1, 2, • • • k} for some k. Similarly, by a k-edge labeling of a graph, we mean a function f from the edges to {1, 2, • • • k} for some k. A k-total labeling is a function f from the set of edges and vertices to {1, 2, • • • k} for some k. A k-vertex labeling is said to be proper if no two adjacent vertices share the same label. Similarly, a k-edge labeling is proper if no two edges that share a vertex share a label. A proper k-total labeling is a k-total labeling such that its corresponding k-edge labeling is proper, its corresponding k-vertex labeling is proper, and no edge has the same label as either of its vertices. Ranjan Rohatgi and Yufei Zhang introduced the idea of a total difference labeling of a graph . Given a graph G, a k-total difference labeling of the graph is a total labeling f from the set of edges and vertices to the set {1, 2, • • • k} satisfying that for any edge {u, v}, f Recall that a total labeling of a graph is a labeling of both the edges and vertices of a graph. In general, f is a function from the union of the edge set and vertex set of G (denoted by E(G) and V (G), respectively) to the set {1, 2, • • • , k}. We will concern ourselves with proper total difference labelings. In a proper k-total difference labeling, f is a function from V (G) ∪ E(G) to the set {1, 2, • • • , k} that satisfies the following properties: 1. For any edge {u, v}, f ({u, v}) = |f (u) -f (v)|. 2. No two adjacent vertices have the same same label. That is, if {u, v} is an edge, then f (u) = f (v).

Next-generation sequencing technologies have redefined the way genome sequencing is performed. They are able to produce tens of millions of short sequences (reads), during a single experiment, and with a much lower cost than previously possible. Due to the dramatic increase in the amount of data generated, a challenging task is to map (align) a set of reads to a reference genome. In this paper, we study a different version of this problem: mapping these reads to a dynamically changing genomic sequence. We propose a new practical algorithm, which employs a suitable data structure that takes into account potential dynamic effects (replacements, insertions, deletions) on the genomic sequence. The presented experimental results demonstrate that the proposed approach can be extended and applied to address the problem of mapping short reads to multiple related genomes.

We propose a new algorithm that solves the Steiner tree problem on graphs with ver- where tw is the graph's treewidth and the Bell number B k is the number of partitions of a k-element set. This is a lineartime algorithm for graphs with fixed treewidth and a polynomial algorithm for tw ∈ O(log |V |/ log log |V |). While being faster than the previously known algorithms, the coloring scheme used in our algorithm can be extended to give new, improved algorithms for the prize-collecting Steiner tree as well as the k-cardinality tree problems with similar runtime bounds.

We propose a new algorithm that solves the Steiner tree problem on graphs with ver- where tw is the graph's treewidth and the Bell number B k is the number of partitions of a k-element set. This is a lineartime algorithm for graphs with fixed treewidth and a polynomial algorithm for tw ∈ O(log |V |/ log log |V |). While being faster than the previously known algorithms, the coloring scheme used in our algorithm can be extended to give new, improved algorithms for the prize-collecting Steiner tree as well as the k-cardinality tree problems with similar runtime bounds.