Related papers: An ETH-Tight FPT Algorithm for Rejection-Proof Set…
Kidney paired donation programs allow patients registered with an incompatible donor to receive a suitable kidney from another donor, as long as the latter's co-registered patient, if any, also receives a kidney from a different donor. The…
Cycle packing is a fundamental problem in optimization, graph theory, and algorithms. Motivated by recent advancements in finding vertex-disjoint paths between a specified set of vertices that either minimize the total length of the paths…
In kidney exchange programs, multiple patient-donor pairs each of whom are otherwise incompatible, exchange their donors to receive compatible kidneys. The Kidney Exchange problem is typically modelled as a directed graph where every vertex…
In this paper, we consider the Cycle Packing problem on unit disk graphs defined as follows. Given a unit disk graph G with n vertices and an integer k, the goal is to find a set of $k$ vertex-disjoint cycles of G if it exists. Our…
Kidney exchange programs (KEPs) form an innovative approach to increasing the donor pool through allowing the participation of renal patients together with a willing but incompatible donor. The aim of a KEP is to identify groups of…
Motivated by kidney exchange, we study a stochastic cycle and chain packing problem, where we aim to identify structures in a directed graph to maximize the expectation of matched edge weights. All edges are subject to failure, and the…
The classical NP-complete problem Vertex Cover requires us to determine whether a graph contains at most $k$ vertices that cover all edges. In spite of its intractability, the problem can be solved in FPT time for parameter $k$ by various…
The kidney exchange mechanism allows many patient-donor pairs who are otherwise incompatible with each other to come together and exchange kidneys along a cycle. However, due to infrastructure and legal constraints, kidney exchange can only…
We introduce the Stackelberg kidney exchange problem. In this problem, an agent (e.g. a hospital or a national organization) has control over a number of incompatible patient-donor pairs whose patients are in need of a transplant. The agent…
The CONTRACTION(vc) problem takes as input a graph $G$ on $n$ vertices and two integers $k$ and $d$, and asks whether one can contract at most $k$ edges to reduce the size of a minimum vertex cover of $G$ by at least $d$. Recently, Lima et…
In Path Set Packing, the input is an undirected graph $G$, a collection $\calp$ of simple paths in $G$, and a positive integer $k$. The problem is to decide whether there exist $k$ edge-disjoint paths in $\calp$. We study the parameterized…
In the \textsc{Maximum Degree Contraction} problem, input is a graph $G$ on $n$ vertices, and integers $k, d$, and the objective is to check whether $G$ can be transformed into a graph of maximum degree at most $d$, using at most $k$ edge…
We introduce and study the complexity of Path Packing. Given a graph $G$ and a list of paths, the task is to embed the paths edge-disjoint in $G$. This generalizes the well known Hamiltonian-Path problem. Since Hamiltonian Path is…
We study a general family of problems that form a common generalization of classic hitting (also referred to as covering or transversal) and packing problems. An instance of X-HitPack asks: Can removing k (deletable) vertices of a graph G…
The starting point of our work is a decade-old open question concerning the subexponential parameterized complexity of \textsc{2-Layer Crossing Minimization}. In this problem, the input is an $n$-vertex graph $G$ whose vertices are…
The Kidney Exchange Problem is a prominent challenge in healthcare and economics, arising in the context of organ transplantation. It has been extensively studied in artificial intelligence and optimization. In a kidney exchange, a set of…
In this paper we consider Simultaneous Feedback Edge Set (Sim-FES) problem. In this problem, the input is an $n$-vertex graph $G$, an integer $k$ and a coloring function ${\sf col}: E(G) \rightarrow 2^{[\alpha]}$ and the objective is to…
In the EDGE CLIQUE COVER (ECC) problem, given a graph G and an integer k, we ask whether the edges of G can be covered with k complete subgraphs of G or, equivalently, whether G admits an intersection model on k-element universe. Gramm et…
Kidney exchange programs (KEP's) represent an additional possibility of transplant for patients suffering from end stage kidney disease. If a patient has a willing living donor with whom the patient is not compatible, the pair…
We consider the problem of packing node-disjoint directed paths in a directed graph. We consider a variant of this problem where each path starts within a fixed subset of root nodes, subject to a given bound on the length of paths. This…