Related papers: Efficiently computing runs on a trie
In this paper we investigate the problem of partitioning an input string T in such a way that compressing individually its parts via a base-compressor C gets a compressed output that is shorter than applying C over the entire T at once.…
Constructing a sparse spanning subgraph is a fundamental primitive in graph theory. In this paper, we study this problem in the Centralized Local model, where the goal is to decide whether an edge is part of the spanning subgraph by…
We consider the standard message passing model; we assume the system is fully synchronous: all processes start at the same time and time proceeds in synchronised rounds. In each round each vertex can transmit a different message of size…
Given a set of strings, the shortest common superstring problem is to find the shortest possible string that contains all the input strings. The problem is NP-hard, but a lot of work has gone into designing approximation algorithms for…
The maximum/minimum bisection problems are, given an edge-weighted graph, to find a bipartition of the vertex set into two sets whose sizes differ by at most one, such that the total weight of edges between the two sets is…
A string is closed if it has length 1 or has a nonempty border without internal occurrences. In this paper we introduce the definition of a \emph{maximal closed substring} (MCS), which is an occurrence of a closed substring that cannot be…
In the semi-streaming model, an algorithm must process any $n$-vertex graph by making one or few passes over a stream of its edges, use $O(n \cdot \text{polylog }n)$ words of space, and at the end of the last pass, output a solution to the…
We obtain upper bounds (in most cases, sharp) for the hitting times of random walks on finite undirected graphs expressed as functions of the graph's number of edges. In particular, we show that the maximum hitting time for a simple random…
The problem of constructing optimal factoring automata arises in the context of unification factoring for the efficient execution of logic programs. Given an ordered set of $n$ strings of length $m$, the problem is to construct a trie-like…
Let C be a linear code with length n and minimum distance d. The stopping redundancy of C is defined as the minimum number of rows in a parity-check matrix for C such that the smallest stopping sets in the corresponding Tanner graph have…
We revisit the problem of finding shortest unique substring (SUS) proposed recently by [6]. We propose an optimal $O(n)$ time and space algorithm that can find an SUS for every location of a string of size $n$. Our algorithm significantly…
In the usual trace reconstruction problem, the goal is to exactly reconstruct an unknown string of length $n$ after it passes through a deletion channel many times independently, producing a set of traces (i.e., random subsequences of the…
A set of segments in the plane may form a Euclidean TSP tour or a matching, among others. Optimal TSP tours as well as minimum weight perfect matchings have no crossing segments, but several heuristics and approximation algorithms may…
Pedigrees, or family trees, are graphs of family relationships that are used to study inheritance. A fundamental problem in computational biology is to find, for a pedigree with $n$ individuals genotyped at every site, a set of…
We present an algorithm computing the longest periodic subsequence of a string of length $n$ in $O(n^7)$ time with $O(n^4)$ words of space. We obtain improvements when restricting the exponents or extending the search allowing the reported…
It is known that any chordal graph on $n$ vertices can be represented as the intersection of $n$ subtrees in a tree on $n$ nodes. This fact is recently used in [2] to generate random chordal graphs on $n$ vertices by generating $n$ subtrees…
A recent work shows how we can optimize a tree based mode of operation for a rate 1 hash function. In particular, an algorithm and a theorem are presented for selecting a good tree topology in order to optimize both the running time and the…
In the standard CONGEST model for distributed network computing, it is known that "global" tasks such as minimum spanning tree, diameter, and all-pairs shortest paths, consume large bandwidth, for their running-time is…
Explorable heap selection is the problem of selecting the $n$th smallest value in a binary heap. The key values can only be accessed by traversing through the underlying infinite binary tree, and the complexity of the algorithm is measured…
The crossing number is the smallest number of pairwise edge-crossings when drawing a graph into the plane. There are only very few graph classes for which the exact crossing number is known or for which there at least exist constant…