Related papers: On Treewidth and Stable Marriage
We consider the problem of finding a subgraph of a given graph which minimizes the sum of given functions at vertices evaluated at their subgraph degrees. While the problem is NP-hard already when all functions are the same, we show that it…
The stable marriage problem with incomplete lists and ties (SMTI) and the hospitals/residents problem with ties (HRT) are important in matching theory with broad practical applications. In this paper, we introduce a tie-breaking based local…
The 3SUM problem is to decide, given a set of $n$ real numbers, whether any three sum to zero. It is widely conjectured that a trivial $O(n^2)$-time algorithm is optimal and over the years the consequences of this conjecture have been…
The classical stable marriage problem asks for a matching between a set of men and a set of women with no blocking pairs, which are pairs formed by a man and a woman who would both prefer switching from their current status to be paired up…
There has been great interest in identifying tractable subclasses of NP complete problems and designing efficient algorithms for these tractable classes. Constraint satisfaction and Bayesian network inference are two examples of such…
In the classical Steiner tree problem, given an undirected, connected graph $G=(V,E)$ with non-negative edge costs and a set of \emph{terminals} $T\subseteq V$, the objective is to find a minimum-cost tree $E' \subseteq E$ that spans the…
We give an algorithm that takes as input an $n$-vertex graph $G$ and an integer $k$, runs in time $2^{O(k^2)} n^{O(1)}$, and outputs a tree decomposition of $G$ of width at most $k$, if such a decomposition exists. This resolves the…
A \emph{binary tanglegram} is a drawing of a pair of rooted binary trees whose leaf sets are in one-to-one correspondence; matching leaves are connected by inter-tree edges. For applications, for example, in phylogenetics, it is essential…
Fixed-parameter tractability analysis and scheduling are two core domains of combinatorial optimization which led to deep understanding of many important algorithmic questions. However, even though fixed-parameter algorithms are appealing…
Given a graph $G$ and a digraph $D$ whose vertices are the edges of $G$, we investigate the problem of finding a spanning tree of $G$ that satisfies the constraints imposed by $D$. The restrictions to add an edge in the tree depend on its…
Many algorithms have been developed for NP-hard problems on graphs with small treewidth $k$. For example, all problems that are expressable in linear extended monadic second order can be solved in linear time on graphs of bounded treewidth.…
We study the optimization version of constraint satisfaction problems (Max-CSPs) in the framework of parameterized complexity; the goal is to compute the maximum fraction of constraints that can be satisfied simultaneously. In standard…
Given a simple graph $G$, a weight function $w:E(G)\rightarrow \mathbb{N} \setminus \{0\}$, and an orientation $D$ of $G$, we define $\mu^-(D) = \max_{v \in V(G)} w_D^-(v)$, where $w^-_D(v) = \sum_{u\in N_D^{-}(v)}w(uv)$. We say that $D$ is…
Given a set of points in the Euclidean plane, the Euclidean \textit{$\delta$-minimum spanning tree} ($\delta$-MST) problem is the problem of finding a spanning tree with maximum degree no more than $\delta$ for the set of points such the…
In the Determinant Maximization problem, given an $n\times n$ positive semi-definite matrix $\bf{A}$ in $\mathbb{Q}^{n\times n}$ and an integer $k$, we are required to find a $k\times k$ principal submatrix of $\bf{A}$ having the maximum…
Orienting the edges of an undirected graph such that the resulting digraph satisfies some given constraints is a classical problem in graph theory, with multiple algorithmic applications. In particular, an $st$-orientation orients each edge…
Treewidth is a graph parameter that plays a fundamental role in several structural and algorithmic results. We study the problem of decomposing a given graph $G$ into node-disjoint subgraphs, where each subgraph has sufficiently large…
We study set selection problems where the weights are uncertain. Instead of its exact weight, only an uncertainty interval containing its true weight is available for each element. In some cases, some solutions are universally optimal;…
Treewidth is a parameter that measures how tree-like a relational instance is, and whether it can reasonably be decomposed into a tree. Many computation tasks are known to be tractable on databases of small treewidth, but computing the…
The performance of distributed and data-centric applications often critically depends on the interconnecting network. Applications are hence modeled as virtual networks, also accounting for resource demands on links. At the heart of…