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Graph spanners are sparse subgraphs that faithfully preserve the distances in the original graph up to small stretch. Spanner have been studied extensively as they have a wide range of applications ranging from distance oracles, labeling…
Recent work has pinned down the existentially optimal size bounds for vertex fault-tolerant spanners: for any positive integer $k$, every $n$-node graph has a $(2k-1)$-spanner on $O(f^{1-1/k} n^{1+1/k})$ edges resilient to $f$ vertex…
Several biological problems require the identification of regions in a sequence where some feature occurs within a target density range: examples including the location of GC-rich regions, identification of CpG islands, and sequence…
The $n$-dimensional binary hypercube is the graph whose vertices are the binary $n$-tuples $\{0, 1\}^n$ and where two vertices are connected by an edge if they differ at exactly one coordinate. We prove that if the edges are assigned…
We introduce the following submodular generalization of the Shortest Cycle problem. For a nonnegative monotone submodular cost function $f$ defined on the edges (or the vertices) of an undirected graph $G$, we seek for a cycle $C$ in $G$ of…
Described are two algorithms to find long approximate palindromes in a string, for example a DNA sequence. A simple algorithm requires O(n)-space and almost always runs in $O(k.n)$-time where n is the length of the string and k is the…
For any integer $n\geq 1$ a middle levels Gray code is a cyclic listing of all $n$-element and $(n+1)$-element subsets of $\{1,2,\ldots,2n+1\}$ such that any two consecutive subsets differ in adding or removing a single element. The…
A generalized Davenport-Schinzel sequence is one over a finite alphabet that contains no subsequences isomorphic to a fixed forbidden subsequence. One of the fundamental problems in this area is bounding (asymptotically) the maximum length…
We consider directed graphs where each edge is labeled with an integer weight and study the fundamental algorithmic question of computing the value of a cycle with minimum mean weight. Our contributions are twofold: (1) First we show that…
Given two sequences $A[1..n]$ and $B[1..m]$ over a totally ordered alphabet, the \emph{Longest Common Bitonic Subsequence} (LCBS) problem asks for a longest common subsequence that is strictly increasing up to a single peak element and…
The order-preserving model (op-model, in short) was introduced quite recently but has already attracted significant attention because of its applications in data analysis. We introduce several types of periods in this setting (op-periods).…
In this paper we consider the time and the crossing sequence complexities of one-tape off-line Turing machines. We show that the running time of each nondeterministic machine accepting a nonregular language must grow at least as n\log n, in…
An order-$s$ Davenport-Schinzel sequence over an $n$-letter alphabet is one avoiding immediate repetitions and alternating subsequences with length $s+2$. The main problem is to determine the maximum length of such a sequence, as a function…
In-place associative integer sorting technique was proposed for integer lists which requires only constant amount of additional memory replacing bucket sort, distribution counting sort and address calculation sort family of algorithms.…
In this paper, we present and study the \emph{Hamming distance oracle problem}. In this problem, the task is to preprocess two strings $S$ and $T$ of lengths $n$ and $m$, respectively, to obtain a data-structure that is able to answer…
We consider the problem of computing a $(1+\epsilon)$-approximation of the Hamming distance between a pattern of length $n$ and successive substrings of a stream. We first look at the one-way randomised communication complexity of this…
Complex orthogonal designs (CODs) are used to construct space-time block codes. COD $\mathcal{O}_z$ with parameter $[p, n, k]$ is a $p \times n$ matrix, where nonzero entries are filled by $\pm z_i$ or $\pm z^*_i$, $i = 1, 2,..., k$, such…
For a given graph G and integers b,f >= 0, let S be a subset of vertices of G of size b+1 such that the subgraph of G induced by S is connected and S can be separated from other vertices of G by removing f vertices. We prove that every…
Classic cycle-joining techniques have found widespread application in creating universal cycles for a diverse range of combinatorial objects, such as shorthand permutations, weak orders, orientable sequences, and various subsets of $k$-ary…
An order-preserving square in a string is a fragment of the form $uv$ where $u\neq v$ and $u$ is order-isomorphic to $v$. We show that a string $w$ of length $n$ over an alphabet of size $\sigma$ contains $\mathcal{O}(\sigma n)$…