Petr Kolman

The greedy algorithm for the minimum common string partition problem

In the Minimum Common String Partition problem (MCSP), we are given two strings on input, and we wish to partition them into the same collection of substrings, minimizing the number of the substrings in the partition. This problem is NP-hard, even for a special case, denoted 2-MCSP, where each letter occurs at most twice in each input string. We study a greedy algorithm for MCSP that at each step extracts a longest common substring from the given strings. We show that the approximation ratio of this algorithm is between Ω(n0.43) and O(n0.69). In the case of 2-MCSP, we show that the approximation ratio is equal to 3. For 4-MCSP, we give a lower bound of Ω(log n).

Minimum common string partition problem: hardness and approximations

String comparison is a fundamental problem in computer science, with applications in areas such as computational biology, text processing or compression In this paper we address the minimum common string partition problem, a string comparison problem with tight connection to the problem of sorting by reversals with duplicates, a key problem in genome rearrangement. n nA partition of a string A is a sequence

Approximating reversal distance for strings with bounded number of duplicates

{mathcal P}=(P_{1},P_{2},...P_{m})

Length-bounded cuts and flows

of strings, called the blocks, whose concatenation is equal to A Given a partition

On the complexity of paths avoiding forbidden pairs

{mathcal P}

Crossing number, pair-crossing number, and expansion

of a string A and a partition

A note on the greedy algorithm for the unsplittable flow problem

{mathcal Q}

Simple on-line algorithms for the maximum disjoint paths problem

of a string B, we say that the pair

Short length Menger's theorem and reliable optical routing

langlemathcal{P,Q}rangle

Reversal distance for strings with duplicates: linear time approximation using hitting set

is a common partition of A and B if