9,715 research outputs found
A Compact DAG for Storing and Searching Maximal Common Subsequences
No full textMaximal Common Subsequences (MCSs) between two strings X and Y are subsequences of both X and Y that are maximal under inclusion. MCSs relax and generalize the well known and widely used concept of Longest Common Subsequences (LCSs), which can be seen as MCSs of maximum length. While the number both LCSs and MCSs can be exponential in the length of the strings, LCSs have been long exploited for string and text analysis, as simple compact representations of all LCSs between two strings, built via dynamic programming or automata, have been known since the '70s. MCSs appear to have a more challenging structure: even listing them efficiently was an open problem open until recently, thus narrowing the complexity difference between the two problems, but the gap remained significant. In this paper we close the complexity gap: we show how to build DAG of polynomial size - in polynomial time - which allows for efficient operations on the set of all MCSs such as enumeration in Constant Amortized Time per solution (CAT), counting, and random access to the i-th element (i.e., rank and select operations). Other than improving known algorithmic results, this work paves the way for new sequence analysis methods based on MCSs
Listing the bonds of a graph in O ̃(n)–delay
No full textGiven a connected graph G = (V, E), with n := |V| vertices and m := |E| edges, a cut can be represented as a bipartition {S, S} of the vertices or as the set of those edges in E having one endpoint in S and the other in S, denoted by 8G(S, S). A cut is minimal, or also called bond, if and only if the two induced subgraphs obtained by removing the edges in the cut are both connected. When the bond separates two given vertices s and t, we talk about s, t-bond. In this work, we consider the problems of listing all the bonds and listing all the s, t-bonds in a graph. These fundamental problems find application in many research areas, such as, beyond graph theory, network reliability, bioinformatics, and chemistry. The state-of-the-art algorithm exploits binary partition to output each s, t-bond in O(m) per bond, being thus classified as an O(m)-delay algorithm. Here we present two new algorithms to address these problems. The first one implements a slightly different branching strategy than the state of the art, though achieving the same complexity. Anyway, we can improve it by relying on dynamic data structures and amortized analysis, obtaining an algorithm that outputs a new bond in O similar to(n). By assuming only the two bond-shores are output for every bond, this is the first outputlinear algorithm listing bonds. In case we commit to explicitly providing the entire edge-set of every bond, the delay becomes O similar to(n) + |8G(S, S)|. (c) 2024 Elsevier B.V. All rights reserved
Listing acyclic subgraphs and subgraphs of bounded girth in directed graphs
No full textThe girth of a directed graph is the length of its shortest directed cycle. We consider the problem of generating all subgraphs of girth at least g in a directed graph G with n vertices and m edges. This generalizes the problem of generating acyclic subgraphs (i.e., with no directed cycle), that correspond to the subgraphs of girth at least n+ 1. The problem of finding the acyclic subgraph with maximum size or weight has been thoroughly studied, however to the best of our knowledge there is no known efficient enumeration algorithm. We propose polynomial delay algorithms for listing both induced and edge subgraphs with girth g in time O(n) per solution; both improve upon a naive solution, respectively by a factor O(nm) and O(m2). Furthermore, this work is on the line of existing research for extracting acyclic structures from graphs
Efficient enumeration of subgraphs and induced subgraphs with bounded girth
No full textThe girth of a graph is the length of its shortest cycle. Due to its relevance in graph theory, network analysis and practical fields such as distributed computing, girth-related problems have been object of attention in both past and recent literature. In this paper, we consider the problem of listing connected subgraphs with bounded girth. As a large girth is index of sparsity, this allows to extract sparse structures from the input graph. We propose two algorithms, for enumerating respectively vertex induced subgraphs and edge induced subgraphs with bounded girth, both running in O(n) amortized time per solution and using space. Furthermore, the algorithms can be easily adapted to relax the connectivity requirement and to deal with weighted graphs. As a byproduct, the second algorithm can be used to answer the well known question of finding the densest n-vertex graph(s) of girth k
Finding Diverse Strings and Longest Common Subsequences in a Graph
No full textIn this paper, we study for the first time the Diverse Longest Common Subsequences (LCSs) problem under Hamming distance. Given a set of a constant number of input strings, the problem asks to decide if there exists some subset X of K longest common subsequences whose diversity is no less than a specified threshold Δ, where we consider two types of diversities of a set X of strings of equal length: the Sum diversity and the Min diversity defined as the sum and the minimum of the pairwise Hamming distance between any two strings in X, respectively. We analyze the computational complexity of the respective problems with Sum- and Min-diversity measures, called the Max-Sum and Max-Min Diverse LCSs, respectively, considering both approximation algorithms and parameterized complexity. Our results are summarized as follows. When K is bounded, both problems are polynomial time solvable. In contrast, when K is unbounded, both problems become NP-hard, while Max-Sum Diverse LCSs problem admits a PTAS. Furthermore, we analyze the parameterized complexity of both problems with combinations of parameters K and r, where r is the length of the candidate strings to be selected. Importantly, all positive results above are proven in a more general setting, where an input is an edge-labeled directed acyclic graph (DAG) that succinctly represents a set of strings of the same length. Negative results are proven in the setting where an input is explicitly given as a set of strings. The latter results are equipped with an encoding such a set as the longest common subsequences of a specific input string set
Efficient Enumeration of Dominating Sets for Sparse Graphs
No full textA dominating set D of a graph G is a set of vertices such that any vertex in G is in D or its neighbor is in D. Enumeration of minimal dominating sets in a graph is one of central problems in enumeration study since enumeration of minimal dominating sets corresponds to enumeration of minimal hypergraph transversal. However, enumeration of dominating sets including non-minimal ones has not been received much attention. In this paper, we address enumeration problems for dominating sets from sparse graphs which are degenerate graphs and graphs with large girth, and we propose two algorithms for solving the problems. The first algorithm enumerates all the dominating sets for a k-degenerate graph in O(k) time per solution using O(n + m) space, where n and m are respectively the number of vertices and edges in an input graph. That is, the algorithm is optimal for graphs with constant degeneracy such as trees, planar graphs, H-minor free graphs with some fixed H. The second algorithm enumerates all the dominating sets in constant time per solution for input graphs with girth at least nine
Spanner Enumeration for Temporal Graphs
No full textA spanner of a temporal graph is a subset of edges that preserves connectivity over time between vertices. A minimal spanner is one in which no additional edges can be removed without breaking this connectivity. Our focus is on enumerating minimal spanners for a given temporal graph. We explore several variations of this problem based on the type of connectivity that must be maintained, ranging from one-to-all connectivity to one-to-all-to-one, many-to-all, and finally all-to-all connectivity. We establish that these problems become progressively harder: (i) We present a polynomial-delay enumeration algorithm for one-to-all connectivity; (ii) We prove Dual-hardness for both one-to-all-to-one and many-to-all connectivity, even in the restricted case of two-to-all; (iii) Finally, for all-to-all connectivity, we show that enumeration cannot be performed in output-polynomial time unless P = NP
UNO News Events, March 2016 Author Linda Suskie Leads Interactive Webinar for Faculty
No full textThe Center for Faculty Excellence and the Assessment Committee will co-sponsor two webinars presented by Linda Suskie, author of Assessing Student Learning: A Common Sense Guide. The assessment webinars will be interactive with a short set of presentations, and each will be followed by a question and answer discussion. The book discussion will focus on Chapter 7--Organizing an Assessment Process and Chapter 10-Creating on Effective Assinment
ColorCoding: Implementation of some algorithms for graph similarity based on the color-coding method by Alon-Yuster-Zwick
No full textNew insights in high-energy electron emission and underlying transport physics of nanocrystalline Si
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