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Fast exact algorithms are known for Hamiltonian paths in undirected and directed bipartite graphs through elegant though involved algorithms that are quite different from each other. We devise algorithms that are simple and similar to each…
In this paper we show that certain special cases of the hidden subgroup problem can be solved in polynomial time by a quantum algorithm. These special cases involve finding hidden normal subgroups of solvable groups and permutation groups,…
Approximate string matching is the problem of finding all factors of a text t of length n that are at a distance at most k from a pattern x of length m. Approximate circular string matching is the problem of finding all factors of t that…
Pattern matching of streaming time series with lower latency under limited computing resource comes to a critical problem, especially as the growth of Industry 4.0 and Industry Internet of Things. However, against traditional single pattern…
Long traces and large event logs that originate from sensors and prediction models are becoming more common in our data-rich world. In such circumstances, conformance checking, a key task in process mining, can become computationally…
The theory of holographic algorithms, which are polynomial time algorithms for certain combinatorial counting problems, yields insight into the hierarchy of complexity classes. In particular, the theory produces algebraic tests for a…
Term pattern matching is the problem of finding all pattern matches in a subject term, given a set of patterns. Finding efficient algorithms for this problem is an important direction for research [19]. We present a new set automaton…
The dictionary matching problem preprocesses a set of patterns and finds all occurrences of each of the patterns in a text when it is provided. We focus on the dynamic setting, in which patterns can be inserted to and removed from the…
Multiple string matching is known as locating all the occurrences of a given number of patterns in an arbitrary string. It is used in bio-computing applications where the algorithms are commonly used for retrieval of information such as…
Bytewise approximate matching algorithms have in recent years shown significant promise in de- tecting files that are similar at the byte level. This is very useful for digital forensic investigators, who are regularly faced with the…
We present an efficient algorithm for finding all approximate occurrences of a given pattern $p$ of length $m$ in a text $t$ of length $n$ allowing for translocations of equal length adjacent factors and inversions of factors. The algorithm…
In this paper we investigate the \emph{approximate string matching problem} when the allowed edit operations are \emph{non-overlapping unbalanced translocations of adjacent factors}. Such kind of edit operations take place when two adjacent…
Holographic algorithms introduced by Valiant are composed of two ingredients: matchgates, which are gadgets realizing local constraint functions by weighted planar perfect matchings, and holographic reductions, which show equivalences among…
In real-world, many problems can be formulated as the alignment between two geometric patterns. Previously, a great amount of research focus on the alignment of 2D or 3D patterns, especially in the field of computer vision. Recently, the…
In the paper, we investigate two problems on strings. The first one is the String matching problem, and the second one is the String comparing problem. We provide a quantum algorithm for the String matching problem that uses exponentially…
Fitting geometric models onto outlier contaminated data is provably intractable. Many computer vision systems rely on random sampling heuristics to solve robust fitting, which do not provide optimality guarantees and error bounds. It is…
In this paper we study a variant of string pattern matching which deals with tuples of strings known as \textit{multi-track strings}. Multi-track strings are a generalisation of strings (or \textit{single-track strings}) that have primarily…
Detectability of failures of linear programming (LP) decoding and the potential for improvement by adding new constraints motivate the use of an adaptive approach in selecting the constraints for the underlying LP problem. In this paper, we…
This paper focuses on integer linear programs where solutions are binary matrices, and the corresponding symmetry group is the set of all column permutations. Orbitopal fixing, as introduced by Kaibel et al., is a technique designed to…
The maximum clique problem is a well known NP-Hard problem with applications in data mining, network analysis, informatics, and many other areas. Although there exist several algorithms with acceptable runtimes for certain classes of…