Related papers: Beyond hypergraph acyclicity: limits of tractabili…
Global polynomial optimization methods typically rely on compactness of the feasible region in order to find solutions. These methods can incur considerable computational expense and most commercially available solvers do not verify the…
We study the neighborhood polynomial and the complexity of its computation for chordal graphs. The neighborhood polynomial of a graph is the generating function of subsets of its vertices that have a common neighbor. We introduce a…
Tree projections provide a unifying framework to deal with most structural decomposition methods of constraint satisfaction problems (CSPs). Within this framework, a CSP instance is decomposed into a number of sub-problems, called views,…
We introduce and study four optimization problems that generalize the well-known subset sum problem. Given a node-weighted digraph, select a subset of vertices whose total weight does not exceed a given budget. Some additional constraints…
We study homomorphism polynomials, which are polynomials that enumerate all homomorphisms from a pattern graph $H$ to $n$-vertex graphs. These polynomials have received a lot of attention recently for their crucial role in several new…
We consider hypergraph network design problems where the goal is to construct a hypergraph that satisfies certain connectivity requirements. For graph network design problems where the goal is to construct a graph that satisfies certain…
Graph polynomials encode fundamental combinatorial invariants of graphs. Their computation is investigated using tree and path decomposition frameworks, with formal definitions of treewidth, k-trees, and pathwidth establishing the…
A Pseudo-Boolean (PB) constraint is a linear inequality constraint over Boolean literals. One of the popular, efficient ideas used to solve PB-problems (a set of PB-constraints) is to translate them to SAT instances (encodings) via, for…
In this paper, we address the scenario where nodes with sensor data are connected in a tree network, and every node wants to compute a given symmetric Boolean function of the sensor data. We first consider the problem of computing a…
We formulate and optimally solve a new generalized Set Similarity Search problem, which assumes the size of the database and query sets are known in advance. By creating polylog copies of our data-structure, we optimally solve any symmetric…
We consider the replica placement problem: given a graph with clients and nodes, place replicas on a minimum set of nodes to serve all the clients; each client is associated with a request and maximum distance that it can travel to get…
We describe a polynomial-time algorithm which, given a graph $G$ with treewidth $t$, approximates the pathwidth of $G$ to within a ratio of $O(t\sqrt{\log t})$. This is the first algorithm to achieve an $f(t)$-approximation for some…
Combining the techniques of approximation algorithms and parameterized complexity has long been considered a promising research area, but relatively few results are currently known. In this paper we study the parameterized approximability…
Brambles were introduced as the dual notion to treewidth, one of the most central concepts of the graph minor theory of Robertson and Seymour. Recently, Grohe and Marx showed that there are graphs G, in which every bramble of order larger…
Clique-width is a well-studied graph parameter owing to its use in understanding algorithmic tractability: if the clique-width of a graph class ${\cal G}$ is bounded by a constant, a wide range of problems that are NP-complete in general…
Polynomial optimization problems over binary variables can be expressed as integer programs using a linearization with extra monomials in addition to those arising in the given polynomial. We characterize when such a linearization yields an…
In the Fully Leafed Induced Subtrees, one is given a graph $G$ and two integers $a$ and $b$ and the question is to find an induced subtree of $G$ with $a$ vertices and at least $b$ leaves. This problem is known to be NP-complete even when…
Branch-and-bound (BnB) algorithms are widely used to solve combinatorial problems, and the performance crucially depends on its branching heuristic.In this work, we consider a typical problem of maximum common subgraph (MCS), and propose a…
Phylogenetic networks are leaf-labelled directed acyclic graphs that are used to describe non-treelike evolutionary histories and are thus a generalization of phylogenetic trees. The hybridization number of a phylogenetic network is the sum…
In recent years much effort has been concentrated towards achieving polynomial time lower bounds on algorithms for solving various well-known problems. A useful technique for showing such lower bounds is to prove them conditionally based on…