Related papers: Conditional Lower Bound for Subgraph Isomorphism w…
In the Set Cover problem, the input is a ground set of $n$ elements and a collection of $m$ sets, and the goal is to find the smallest sub-collection of sets whose union is the entire ground set. The fastest algorithm known runs in time…
In this paper we study a natural generalization of both {\sc $k$-Path} and {\sc $k$-Tree} problems, namely, the {\sc Subgraph Isomorphism} problem. In the {\sc Subgraph Isomorphism} problem we are given two graphs $F$ and $G$ on $k$ and $n$…
The maximum common subtree isomorphism problem asks for the largest possible isomorphism between subtrees of two given input trees. This problem is a natural restriction of the maximum common subgraph problem, which is ${\sf NP}$-hard in…
We give almost tight conditional lower bounds on the running time of the kHyperPath problem. Given an $r$-uniform hypergraph for some integer $r$, kHyperPath seeks a tight path of length $k$. That is, a sequence of $k$ nodes such that every…
The Subgraph Isomorphism problem is of considerable importance in computer science. We examine the problem when the pattern graph H is of bounded treewidth, as occurs in a variety of applications. This problem has a well-known algorithm via…
Two kinds of approximation algorithms exist for the k-BALANCED PARTITIONING problem: those that are fast but compute unsatisfying approximation ratios, and those that guarantee high quality ratios but are slow. In this paper we prove that…
In the PATH COVER problem, one asks to cover the vertices of a graph using the smallest possible number of (not necessarily disjoint) paths. While the variant where the paths need to be pairwise vertex-disjoint, which we call PATH…
We give a new fpt algorithm testing isomorphism of $n$-vertex graphs of tree width $k$ in time $2^{k\operatorname{polylog} (k)}\operatorname{poly} (n)$, improving the fpt algorithm due to Lokshtanov, Pilipczuk, Pilipczuk, and Saurabh (FOCS…
Given a graph $G=(V,E)$ with non-negative real edge lengths and an integer parameter $k$, the Min-Max k-Tree Cover problem seeks to find a set of at most $k$ subtrees of $G$, such that the union of the trees is the vertex set $V$. The…
In the Densest k-Subgraph problem, given a graph G and a parameter k, one needs to find a subgraph of G induced on k vertices that contains the largest number of edges. There is a significant gap between the best known upper and lower…
In the $K_r$-Cover problem, given a graph $G$ and an integer $k$ one has to decide if there exists a set of at most $k$ vertices whose removal destroys all $r$-cliques of $G$. In this paper we give an algorithm for $K_r$-Cover that runs in…
A connected graph has a $(k,\ell)$-cover if each of its edges is contained in at least $\ell$ cliques of order $k$. Motivated by recent advances in extremal combinatorics and the literature on edge modification problems, we study the…
The Subgraph Isomorphism problem asks, given a host graph G on n vertices and a pattern graph P on k vertices, whether G contains a subgraph isomorphic to P. The restriction of this problem to planar graphs has often been considered. After…
The complexity of the maximum common connected subgraph problem in partial $k$-trees is still not fully understood. Polynomial-time solutions are known for degree-bounded outerplanar graphs, a subclass of the partial $2$-trees. On the other…
We consider the following two algorithmic problems: given a graph $G$ and a subgraph $H\subseteq G$, decide whether $H$ is an isometric or a geodesically convex subgraph of $G$. It is relatively easy to see that the problems can be solved…
For an undirected graph G, we consider the following problems: given a fixed graph H, can we partition the vertices of G into two non-empty sets A and B such that neither the induced graph G[A] nor G[B] contain H (i) as a subgraph? (ii) as…
We extend Babai's quasipolynomial-time graph isomorphism test (STOC 2016) and develop a quasipolynomial-time algorithm for the multiple-coset isomorphism problem. The algorithm for the multiple-coset isomorphism problem allows to exploit…
We investigate the complexity of several fundamental polynomial-time solvable problems on graphs and on matrices, when the given instance has low treewidth; in the case of matrices, we consider the treewidth of the graph formed by non-zero…
For any fixed graph $G$, the subgraph isomorphism problem asks whether an $n$-vertex input graph has a subgraph isomorphic to $G$. A well-known algorithm of Alon, Yuster and Zwick (1995) efficiently reduces this to the "colored" version of…
The Minimum Size Tree Decomposition (MSTD) and Minimum Size Path Decomposition (MSPD) problems ask for a given n-vertex graph G and integer k, what is the minimum number of bags of a tree decomposition (respectively, path decomposition) of…