Related papers: A Polynomial-Time Deterministic Algorithm for an N…
In this paper, we study the problem of optimal multi-robot path planning (MPP) on graphs. We propose two multiflow based integer linear programming (ILP) models that computes minimum last arrival time and minimum total distance solutions…
Bir\'{o} et al. (1992) introduced $H$-graphs, intersection graphs of connected subgraphs of a subdivision of a graph $H$. They are related to many classes of geometric intersection graphs, e.g., interval graphs, circular-arc graphs, split…
A Dynamic Programming based polynomial worst case time and space algorithm is described for computing Hamiltonian Path of a directed graph. Complexity constructive proofs along with a tested C++ implementation are provided as well. The…
In this paper we show a deterministic parallel all-pairs shortest paths algorithm for real-weighted directed graphs. The algorithm has $\tilde{O}(nm+(n/d)^3)$ work and $\tilde{O}(d)$ depth for any depth parameter $d\in [1,n]$. To the best…
Finding a shortest path in a graph is one of the most classic problems in algorithmic and graph theory. While we dispose of quite efficient algorithms for this ordinary problem (like the Dijkstra or Bellman-Ford algorithms), some slight…
The problem of finding multiple simple shortest paths in a weighted directed graph $G=(V,E)$ has many applications, and is considerably more difficult than the corresponding problem when cycles are allowed in the paths. Even for a single…
For a connected graph $G=(V,E)$, a matching $M\subseteq E$ is a matching cut of $G$ if $G-M$ is disconnected. It is known that for an integer $d$, the corresponding decision problem Matching Cut is polynomial-time solvable for graphs of…
We study two variants of \textsc{Maximum Cut}, which we call \textsc{Connected Maximum Cut} and \textsc{Maximum Minimal Cut}, in this paper. In these problems, given an unweighted graph, the goal is to compute a maximum cut satisfying some…
We present three new complexity results for classes of planning problems with simple causal graphs. First, we describe a polynomial-time algorithm that uses macros to generate plans for the class 3S of planning problems with binary state…
Let $G$ be a graph having a vertex $v$ such that $H = G - v$ is a trivially perfect graph. We give a polynomial-time algorithm for the problem of deciding whether it is possible to add at most $k$ edges to $G$ to obtain a trivially perfect…
A dominating set of a graph G(V, E) is a set of vertices D\subseteq V such that every vertex in V\D has a neighbor in D. An eternal dominating set extends this concept by placing mobile guards on the vertices of D. In response to an…
Let $G=(V,E)$ be a finite undirected graph. An edge set $E' \subseteq E$ is a dominating induced matching (d.i.m.) in $G$ if every edge in $E$ is intersected by exactly one edge of $E'$. The Dominating Induced Matching (DIM) problem asks…
We introduce a problem class we call Polynomial Constraint Satisfaction Problems, or PCSP. Where the usual CSPs from computer science and optimization have real-valued score functions, and partition functions from physics have monomials,…
The Maximum Clique Problem (MCP) is a foundational NP-hard problem with wide-ranging applications, yet no single algorithm consistently outperforms all others across diverse graph instances. This underscores the critical need for…
Although NP-Complete problems are the most difficult decisional problems, it is possible to discover in them polynomial (or easy) observables. We study the Graph Partitioning Problem showing that it is possible to recognize in it two…
A polynomial time algorithm which detects all paths and cycles of all lengths in form of vertex pairs (start, finish).
We give a polynomial-time algorithm for detecting very long cycles in dense regular graphs. Specifically, we show that, given $\alpha \in (0,1)$, there exists a $c=c(\alpha)$ such that the following holds: there is a polynomial-time…
Given an integer $k$ and a graph where every edge is colored either red or blue, the goal of the exact matching problem is to find a perfect matching with the property that exactly $k$ of its edges are red. Soon after Papadimitriou and…
Covering all edges of a graph by a small number of vertices, this is the NP-complete Vertex Cover problem. It is among the most fundamental graph-algorithmic problems. Following a recent trend in studying temporal graphs (a sequence of…
In this thesis, we present new techniques to deal with fundamental algorithmic graph problems where graphs are directed and partially dynamic, i.e. undergo either a sequence of edge insertions or deletions: - Single-Source Reachability…