Related papers: If the Current Clique Algorithms are Optimal, so i…
A graph $G=(V,E)$ is a {\it unipolar graph} if there exits a partition $V=V_1 \cup V_2$ such that, $V_1$ is a clique and $V_2$ induces the disjoint union of cliques. The complement-closed class of {\it generalized split graphs} are those…
Mining cohesive subgraphs from a graph is a fundamental problem in graph data analysis. One notable cohesive structure is $\gamma$-quasi-clique (QC), where each vertex connects at least a fraction $\gamma$ of the other vertices inside.…
N-fold integer programming is a fundamental problem with a variety of natural applications in operations research and statistics. Moreover, it is universal and provides a new, variable-dimension, parametrization of all of integer…
We investigate parameterizing hard combinatorial problems by the size of the solution set compared to all solution candidates. Our main result is a uniform sampling algorithm for satisfying assignments of 2-CNF formulas that runs in…
We consider the k-disjoint-clique problem. The input is an undirected graph G in which the nodes represent data items, and edges indicate a similarity between the corresponding items. The problem is to find within the graph k disjoint…
The Maximum Matching problem has a quantum query complexity lower bound of $\Omega(n^{3/2})$ for graphs on $n$ vertices represented by an adjacency matrix. The current best quantum algorithm has the query complexity $O(n^{7/4})$, which is…
Is detecting a $k$-clique in $k$-partite regular (hyper-)graphs as hard as in the general case? Intuition suggests yes, but proving this -- especially for hypergraphs -- poses notable challenges. Concretely, we consider a strong notion of…
We study the Matrix Multiplication Verification Problem (MMV) where the goal is, given three $n \times n$ matrices $A$, $B$, and $C$ as input, to decide whether $AB = C$. A classic randomized algorithm by Freivalds (MFCS, 1979) solves MMV…
A graph is inductive $k$-independent if there exists and ordering of its vertices $v_{1},...,v_{n}$ such that $\alpha(G[N(v_{i})\cap V_{i}])\leq k $ where $N(v_{i})$ is the neighborhood of $v_{i}$, $V_{i}=\{v_{i},...,v_{n}\}$ and $\alpha$…
We study the time complexity of induced subgraph isomorphism problems where the pattern graph is fixed. The earliest known example of an improvement over trivial algorithms is by Itai and Rodeh (1978) who sped up triangle detection in…
Given a graph $G$, let $vc(G)$ and $vc^+(G)$ be the sizes of a minimum and a maximum minimal vertex covers of $G$, respectively. We say that $G$ is well covered if $vc(G)=vc^+(G)$ (that is, all minimal vertex covers have the same size).…
A string matching -- and more generally, sequence matching -- algorithm is presented that has a linear worst-case computing time bound, a low worst-case bound on the number of comparisons (2n), and sublinear average-case behavior that is…
The {Congested Clique} is a distributed-computing model for single-hop networks with restricted bandwidth that has been very intensively studied recently. It models a network by an $n$-vertex graph in which any pair of vertices can…
We consider several well-studied problems in dynamic algorithms and prove that sufficient progress on any of them would imply a breakthrough on one of five major open problems in the theory of algorithms: 1. Is the 3SUM problem on $n$…
Cardinality Maximum Flow Network Interdiction Problem (CMFNIP) is known to be strongly NP-hard problem in the literature. A particular case of CMFNIP has been shown to have reduction from clique problem. In the present work,an effort is…
The problem of finding large cliques in random graphs and its "planted" variant, where one wants to recover a clique of size $\omega \gg \log{(n)}$ added to an \Erdos-\Renyi graph $G \sim G(n,\frac{1}{2})$, have been intensely studied.…
String matching is a fundamental problem in computer science, with critical applications in text retrieval, bioinformatics, and data analysis. Among the numerous solutions that have emerged for this problem in recent decades,…
Sublinear time quantum algorithms have been established for many fundamental problems on strings. This work demonstrates that new, faster quantum algorithms can be designed when the string is highly compressible. We focus on two popular and…
The problem of efficient multiplication of large numbers has been a long-standing challenge in classical computation and has been extensively studied for centuries. It appears that the existing classical algorithms are close to their…
Permutation patterns and pattern avoidance have been intensively studied in combinatorics and computer science, going back at least to the seminal work of Knuth on stack-sorting (1968). Perhaps the most natural algorithmic question in this…