arXiv subjects

Alexandru Popa

Publications and source records attributed to Alexandru Popa.

34 records · Page 2Linked to original sources

arXiv2019

NewsCompare - a novel application for detecting news influence in a country

The concept of `fake news' has been referenced and thrown around in news reports so much in recent years that it has become a news topic in its own right. At its core, it poses a chilling question -- what do we do if our worldview is fundamentally wrong? Even if internally consistent, what if it does not match the real world? Are our beliefs justified, or could we become indoctrinated from living in a `bubble'? If the latter is true, how could we even test the limits of said bubble from within its confines? We propose a new method to augment the process of identifying fake news, by speeding up and automating the more cumbersome and time-consuming tasks involved. Our application, NewsCompare takes any list of target websites as input (news-related in our use case, but otherwise not restricted), visits them in parallel and retrieves any text content found within. Web pages are subsequently compared to each other, and similarities are tentatively pointed out. These results can be manually verified in order to determine which websites tend to draw inspiration from one another. The data gathered on every intermediate step can be queried and analyzed separately, and most notably we already use the set of hyperlinks to and from the various websites we encounter to paint a sort of `map' of that particular slice of the web. This map can then be cross-referenced and further strengthen the conclusion that a particular grouping of sites with strong links to each other, and posting similar content, are likely to share the same allegiance. We run our application on the Romanian news websites and we draw several interesting observations.

cs.SI↗

arXiv2018

Heuristic algorithms for the min-max edge 2-coloring problem

In multi-channel Wireless Mesh Networks (WMN), each node is able to use multiple non-overlapping frequency channels. Raniwala et al. (MC2R 2004, INFOCOM 2005) propose and study several such architectures in which a computer can have multiple network interface cards. These architectures are modeled as a graph problem named \emph{maximum edge $q$-coloring} and studied in several papers by Feng et. al (TAMC 2007), Adamaszek and Popa (ISAAC 2010, JDA 2016). Later on Larjomaa and Popa (IWOCA 2014, JGAA 2015) define and study an alternative variant, named the \emph{min-max edge $q$-coloring}. The above mentioned graph problems, namely the maximum edge $q$-coloring and the min-max edge $q$-coloring are studied mainly from the theoretical perspective. In this paper, we study the min-max edge 2-coloring problem from a practical perspective. More precisely, we introduce, implement and test four heuristic approximation algorithms for the min-max edge $2$-coloring problem. These algorithms are based on a \emph{Breadth First Search} (BFS)-based heuristic and on \emph{local search} methods like basic \emph{hill climbing}, \emph{simulated annealing} and \emph{tabu search} techniques, respectively. Although several algorithms for particular graph classes were proposed by Larjomaa and Popa (e.g., trees, planar graphs, cliques, bi-cliques, hypergraphs), we design the first algorithms for general graphs. We study and compare the running data for all algorithms on Unit Disk Graphs, as well as some graphs from the DIMACS vertex coloring benchmark dataset.

cs.DS↗

arXiv2018

Analytic Geometry of Homogeneous Spaces

The theory uses methods and language of linear algebra to study nonlinear spaces. These techniques can be used particularly to describe analytic geometry of non-linear elliptic, hyperbolic, De Sitter and Anti de Sitter spaces. The main innovation of elaborated theory is space parameterization by introduction of space signature. This parameterization allows studying of different homogeneous spaces in one global framework. When the parameters are used as variables in definitions, axioms, equations, theorems, proofs, all these have exactly the same form that describes the reality of all homogeneous spaces simultaneously. When it is necessary to describe some space particularities or to see the difference between two concrete spaces, the concrete values can be put in parameters of each definition, axiom, equation, theorem and proof.

math.HO↗

arXiv2018

Hardness and algorithmic results for the approximate cover problem

In CPM 2017, Amir et al. introduce a problem, named \emph{approximate string cover} (\textbf{ACP}), motivated by many aplications including coding and automata theory, formal language theory, combinatorics and molecular biology. A \emph{cover} of a string $T$ is a string $C$ for which every letter of $T$ lies within some occurrence of $C$. The input of the \textbf{ACP} problem consists of a string $T$ and an integer $m$ (less than the length of $T$), and the goal is to find a string $C$ of length $m$ that covers a string $T'$ which is as close to $T$ as possible (under some predefined distance). Amir et al. study the problem for the Hamming distance. In this paper we continue the work of Amir et al. and show the following results: We show an approximation algorithm for the \textbf{ACP} with an approximation ratio of $\sqrt{OPT}$, where OPT is the size of the optimal solution. We provide an FPT algorithm with respect to the alphabet size. \item The \textbf{ACP} problem naturally extends to pseudometrics. Moreover, we show that for some family of pseudometrics, that we term \emph{homogenous additive pseudometrics}, the complexity of \textbf{ACP} remains unchanged. We partially give an answer to an open problem of Amir et al. and show that the Hamming distance over an unbounded alphabet is equivalent to an extended metric over a fixed sized alphabet.

cs.DS↗

arXiv2018

A connection between String Covers and Cover Deterministic Finite Tree Automata Minimization

Data compression plays a crucial part in the cloud based systems of today. One the fundaments of compression is quasi-periodicity, for which there are several models. We build upon the most popular quasi-periodicity model for strings, i.e., covers, generalizing it to trees. We introduce a new type of cover automata, which we call \textbf{D}eterministic \textbf{T}ree \textbf{A}utomata. Then, we formulate a cover problem on these DTA and study its complexity, in both sequential and parallel settings. We obtain bounds for the Cover Minimization Problem. Along the way, we uncover an interesting application, the Shortest Common Cover Problem, for which we give an optimal solution.

cs.DS↗

arXiv2018

A quasi linear-time b-Matching algorithm on distance-hereditary graphs and bounded split-width graphs

We present a quasi linear-time algorithm for Maximum Matching on distance-hereditary graphs and some of their generalizations. This improves on [Dragan, WG'97], who proposed such an algorithm for the subclass of (tent,hexahedron)-free distance-hereditary graphs. Furthermore, our result is derived from a more general one that is obtained for b-Matching. In the (unit cost) b-Matching problem, we are given a graph G = (V, E) together with a nonnegative integer capacity b v for every vertex v $\in$ V. The objective is to assign nonnegative integer weights (x e) e$\in$E so that: for every v $\in$ V the sum of the weights of its incident edges does not exceed b v , and e$\in$E x e is maximized. We present the first algorithm for solving b-Matching on cographs, distance-hereditary graphs and some of their generalizations in quasi linear time. For that, we use a decomposition algorithm that outputs for any graph G a collection of subgraphs of G with no edge-cutsets inducing a complete bipartite subgraph (a.k.a., splits). The latter collection is sometimes called a split decomposition of G. Furthermore, there exists a generic method in order to design graph algorithms based on split decomposition [Rao, DAM'08]. However, this technique only applies to "localized" problems: for which a "best" partial solution for any given subgraph in a split decomposition can be computed almost independently from the remaining of the graph. Such framework does not apply to matching problems since an augmenting path may cross the subgraphs arbitrarily. We introduce a new technique that somehow captures all the partial solutions for a given union of subgraphs in a split decomposition, in a compact and amenable way for algorithms - assuming some piecewise linear assumption holds on the value of such solutions. The latter assumption is shown to hold for b-Matching. Doing so, we prove that solving b-Matching on any pair G, b can be reduced in quasi linear-time to solving this problem on a collection of smaller graphs: that are obtained from the subgraphs in any split decomposition of G by replacing every vertex with a constant-size module. In particular, if G has a split decomposition where all subgraphs have order at most a fixed k, then we can solve b-Matching for G, b in O((k log 2 k)$\times$(m+n)$\times$log ||b|| 1)-time. This answers an open question of [Coudert et al., SODA'18].

cs.DS↗

arXiv2018

The use of a pruned modular decomposition for Maximum Matching algorithms on some graph classes

We address the following general question: given a graph class C on which we can solve Maximum Matching in (quasi) linear time, does the same hold true for the class of graphs that can be modularly decomposed into C ? A major difficulty in this task is that the Maximum Matching problem is not preserved by quotient, thereby making difficult to exploit the structural properties of the quotient subgraphs of the modular decomposition. So far, we are only aware of a recent framework in [Coudert et al., SODA'18] that only applies when the quotient subgraphs have bounded order and/or under additional assumptions on the nontriv-ial modules in the graph. As a first attempt toward improving this framework we study the combined effect of modular decomposition with a pruning process over the quotient subgraphs. More precisely, we remove sequentially from all such subgraphs their so-called one-vertex extensions (i.e., pendant, anti-pendant, twin, universal and isolated vertices). Doing so, we obtain a "pruned modular decomposition", that can be computed in O(m log n)-time. Our main result is that if all the pruned quotient subgraphs have bounded order then a maximum matching can be computed in linear time. This result is mostly based on two pruning rules on pendant and anti-pendant modules -- that are adjacent, respectively, to one or all but one other modules in the graph. Furthermore, these two latter rules are surprisingly intricate and we consider them as our main technical contribution in the paper. We stress that the class of graphs that can be totally decomposed by the pruned modular decomposition contains all the distance-hereditary graphs, and so, it is larger than cographs. In particular, as a byproduct of our approach we also obtain the first known linear-time algorithms for Maximum Matching on distance-hereditary graphs and graphs with modular-treewidth at most one. Finally, we can use an extended version of our framework in order to compute a maximum matching, in linear-time, for all graph classes that can be modularly decomposed into cycles. Our work is the first to explain why the existence of some nice ordering over the modules of a graph, instead of just over its vertices, can help to speed up the computation of maximum matchings on some graph classes.

cs.DS↗

arXiv2017

Fully polynomial FPT algorithms for some classes of bounded clique-width graphs

Parameterized complexity theory has enabled a refined classification of the difficulty of NP-hard optimization problems on graphs with respect to key structural properties, and so to a better understanding of their true difficulties. More recently, hardness results for problems in P were achieved using reasonable complexity theoretic assumptions such as: Strong Exponential Time Hypothesis (SETH), 3SUM and All-Pairs Shortest-Paths (APSP). According to these assumptions, many graph theoretic problems do not admit truly subquadratic algorithms, nor even truly subcubic algorithms (Williams and Williams, FOCS 2010 and Abboud, Grandoni, Williams, SODA 2015). A central technique used to tackle the difficulty of the above mentioned problems is fixed-parameter algorithms for polynomial-time problems with polynomial dependency in the fixed parameter (P-FPT). This technique was introduced by Abboud, Williams and Wang in SODA 2016 and continued by Husfeldt (IPEC 2016) and Fomin et al. (SODA 2017), using the treewidth as a parameter. Applying this technique to clique-width, another important graph parameter, remained to be done. In this paper we study several graph theoretic problems for which hardness results exist such as cycle problems (triangle detection, triangle counting, girth, diameter), distance problems (diameter, eccentricities, Gromov hyperbolicity, betweenness centrality) and maximum matching. We provide hardness results and fully polynomial FPT algorithms, using clique-width and some of its upper-bounds as parameters (split-width, modular-width and $P\_4$-sparseness). We believe that our most important result is an ${\cal O}(k^4 \cdot n + m)$-time algorithm for computing a maximum matching where $k$ is either the modular-width or the $P\_4$-sparseness. The latter generalizes many algorithms that have been introduced so far for specific subclasses such as cographs, $P\_4$-lite graphs, $P\_4$-extendible graphs and $P\_4$-tidy graphs. Our algorithms are based on preprocessing methods using modular decomposition, split decomposition and primeval decomposition. Thus they can also be generalized to some graph classes with unbounded clique-width.

cs.DS↗

arXiv2015

Parameterized Complexity of Asynchronous Border Minimization

Microarrays are research tools used in gene discovery as well as disease and cancer diagnostics. Two prominent but challenging problems related to microarrays are the Border Minimization Problem (BMP) and the Border Minimization Problem with given placement (P-BMP). In this paper we investigate the parameterized complexity of natural variants of BMP and P-BMP under several natural parameters. We show that BMP and P-BMP are in FPT under the following two combinations of parameters: 1) the size of the alphabet (c), the maximum length of a sequence (string) in the input (l) and the number of rows of the microarray (r); and, 2) the size of the alphabet and the size of the border length (o). Furthermore, P-BMP is in FPT when parameterized by c and l. We complement our tractability results with corresponding hardness results.

cs.DS↗

arXiv2014

A Parameterized Study of Maximum Generalized Pattern Matching Problems

The generalized function matching (GFM) problem has been intensively studied starting with [Ehrenfeucht and Rozenberg, 1979]. Given a pattern p and a text t, the goal is to find a mapping from the letters of p to non-empty substrings of t, such that applying the mapping to p results in t. Very recently, the problem has been investigated within the framework of parameterized complexity [Fernau, Schmid, and Villanger, 2013]. In this paper we study the parameterized complexity of the optimization variant of GFM (called Max-GFM), which has been introduced in [Amir and Nor, 2007]. Here, one is allowed to replace some of the pattern letters with some special symbols "?", termed wildcards or don't cares, which can be mapped to an arbitrary substring of the text. The goal is to minimize the number of wildcards used. We give a complete classification of the parameterized complexity of Max-GFM and its variants under a wide range of parameterizations, such as, the number of occurrences of a letter in the text, the size of the text alphabet, the number of occurrences of a letter in the pattern, the size of the pattern alphabet, the maximum length of a string matched to any pattern letter, the number of wildcards and the maximum size of a string that a wildcard can be mapped to.

cs.CC↗

arXiv2013

Algorithmic and Hardness Results for the Colorful Components Problems

In this paper we investigate the colorful components framework, motivated by applications emerging from comparative genomics. The general goal is to remove a collection of edges from an undirected vertex-colored graph $G$ such that in the resulting graph $G'$ all the connected components are colorful (i.e., any two vertices of the same color belong to different connected components). We want $G'$ to optimize an objective function, the selection of this function being specific to each problem in the framework. We analyze three objective functions, and thus, three different problems, which are believed to be relevant for the biological applications: minimizing the number of singleton vertices, maximizing the number of edges in the transitive closure, and minimizing the number of connected components. Our main result is a polynomial time algorithm for the first problem. This result disproves the conjecture of Zheng et al. that the problem is $ NP$-hard (assuming $P \neq NP$). Then, we show that the second problem is $ APX$-hard, thus proving and strengthening the conjecture of Zheng et al. that the problem is $ NP$-hard. Finally, we show that the third problem does not admit polynomial time approximation within a factor of $|V|^{1/14 - ε}$ for any $ε> 0$, assuming $P \neq NP$ (or within a factor of $|V|^{1/2 - ε}$, assuming $ZPP \neq NP$).

cs.DS↗

arXiv2013

The min-max edge q-coloring problem

In this paper we introduce and study a new problem named \emph{min-max edge $q$-coloring} which is motivated by applications in wireless mesh networks. The input of the problem consists of an undirected graph and an integer $q$. The goal is to color the edges of the graph with as many colors as possible such that: (a) any vertex is incident to at most $q$ different colors, and (b) the maximum size of a color group (i.e. set of edges identically colored) is minimized. We show the following results: 1. Min-max edge $q$-coloring is NP-hard, for any $q \ge 2$. 2. A polynomial time exact algorithm for min-max edge $q$-coloring on trees. 3. Exact formulas of the optimal solution for cliques and almost tight bounds for bicliques and hypergraphs. 4. A non-trivial lower bound of the optimal solution with respect to the average degree of the graph. 5. An approximation algorithm for planar graphs.

cs.DS↗

arXiv2010

Hardness and Approximation of The Asynchronous Border Minimization Problem

We study a combinatorial problem arising from microarrays synthesis. The synthesis is done by a light-directed chemical process. The objective is to minimize unintended illumination that may contaminate the quality of experiments. Unintended illumination is measured by a notion called border length and the problem is called Border Minimization Problem (BMP). The objective of the BMP is to place a set of probe sequences in the array and find an embedding (deposition of nucleotides/residues to the array cells) such that the sum of border length is minimized. A variant of the problem, called P-BMP, is that the placement is given and the concern is simply to find the embedding. Approximation algorithms have been previously proposed for the problem but it is unknown whether the problem is NP-hard or not. In this paper, we give a thorough study of different variations of BMP by giving NP-hardness proofs and improved approximation algorithms. We show that P-BMP, 1D-BMP, and BMP are all NP-hard. Contrast with the previous result that 1D-P-BMP is polynomial time solvable, the interesting implications include (i) the array dimension (1D or 2D) differentiates the complexity of P-BMP; (ii) for 1D array, whether placement is given differentiates the complexity of BMP; (iii) BMP is NP-hard regardless of the dimension of the array. Another contribution of the paper is improving the approximation for BMP from $O(n^{1/2} \log^2 n)$ to $O(n^{1/4} \log^2 n)$, where $n$ is the total number of sequences.

cs.DS↗

arXiv2010

Uniform Model of Geometric Spaces

Author developed a uniform model for different spaces where distance and angle measure kinds are parameters. This model is calculus centric, but can also be used in theoretical research. It is useful in the following domains: deduction of uniform equations among geometric spaces, uniform model applied to any space, which provides an easy way to calculate distances, plane and dihedral angles of any dimension, areas and volumes as well as parallel (where applied) and orthogonal property detection, study of not yet described spaces and more.

math.MG↗

arXiv2010

Restricted Common Superstring and Restricted Common Supersequence

The {\em shortest common superstring} and the {\em shortest common supersequence} are two well studied problems having a wide range of applications. In this paper we consider both problems with resource constraints, denoted as the Restricted Common Superstring (shortly \textit{RCSstr}) problem and the Restricted Common Supersequence (shortly \textit{RCSseq}). In the \textit{RCSstr} (\textit{RCSseq}) problem we are given a set $S$ of $n$ strings, $s_1$, $s_2$, $\ldots$, $s_n$, and a multiset $t = \{t_1, t_2, \dots, t_m\}$, and the goal is to find a permutation $π: \{1, \dots, m\} \to \{1, \dots, m\}$ to maximize the number of strings in $S$ that are substrings (subsequences) of $π(t) = t_{π(1)}t_{π(2)}...t_{π(m)}$ (we call this ordering of the multiset, $π(t)$, a permutation of $t$). We first show that in its most general setting the \textit{RCSstr} problem is {\em NP-complete} and hard to approximate within a factor of $n^{1-ε}$, for any $ε> 0$, unless P = NP. Afterwards, we present two separate reductions to show that the \textit{RCSstr} problem remains NP-Hard even in the case where the elements of $t$ are drawn from a binary alphabet or for the case where all input strings are of length two. We then present some approximation results for several variants of the \textit{RCSstr} problem. In the second part of this paper, we turn to the \textit{RCSseq} problem, where we present some hardness results, tight lower bounds and approximation algorithms.

cs.DS↗

arXiv2009

Undecidability Results for Finite Interactive Systems

A new approach to the design of massively parallel and interactive programming languages has been recently proposed using rv-systems (interactive systems with registers and voices) and Agapia programming. In this paper we present a few theoretical results on FISs (finite interactive systems), the underlying mechanism used for specifying control and interaction in these systems. First, we give a proof for the undecidability of the emptiness problem for FISs, by reduction to the Post Correspondence Problem. Next, we use the construction in this proof to get other undecidability results, e.g., for the accessibility of a transition in a FIS, or for the finiteness of the language recognized by a FIS. Finally, we present a simple proof of the equivalence between FISs and tile systems, making explicit that they precisely capture recognizable two-dimensional languages.

cs.FL↗