Related papers: A simple deterministic near-linear time approximat…
The intersection graph of a collection of trapezoids with corner points lying on two parallel lines is called a trapezoid graph. These graphs and their generalizations were applied in various fields, including modeling channel routing…
Given an undirected graph $G=(V,E)$ with edge capacities $c_e\geq 1$ for $e\in E$ and a subset $T$ of $k$ vertices called terminals, we say that a graph $H$ is a quality-$q$ cut sparsifier for $G$ iff $T\subseteq V(H)$, and for any…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
Consider a graph $G = (V, E)$ and some commuters, each specified by a tuple $(u, v, b)$ consisting of two nodes in the graph $u, v \in V$ and a non-negative real number $b$, specifying their budget. The goal is to find a pricing function…
The Constraint Shortest Path (CSP) problem is as follows. An $n$-vertex graph is given, each edge/arc assigned two weights. Let us call them "cost" and "length" for definiteness. Finding a min-cost upper-bounded length path between a given…
We give a nearly optimal sublinear-time algorithm for approximating the size of a minimum vertex cover in a graph G. The algorithm may query the degree deg(v) of any vertex v of its choice, and for each 1 <= i <= deg(v), it may ask for the…
Given a graph with edge costs and vertex profits and given a budget B, the Orienteering Problem asks for a walk of cost at most B of maximum profit. Additionally, each profit may be given with a time window within it can be collected by the…
Given a point set $P$ in the plane, we seek a subset $Q\subseteq P$, whose convex hull gives a smaller and thus simpler representation of the convex hull of $P$. Specifically, let $cost(Q,P)$ denote the Hausdorff distance between the convex…
In a temporal graph the edge set dynamically changes over time according to a set of time-labels associated with each edge that indicates at which time-steps the edge is available. Two vertices are connected if there is a path connecting…
Klinz and Woeginger (1995) prove that the minimum cost quickest flow problem is NP-hard. On the other hand, the quickest minimum cost flow problem can be solved efficiently via a straightforward reduction to the quickest flow problem…
We consider the problem of finding an edge in a hidden undirected graph $G = (V, E)$ with $n$ vertices, in a model where we only allowed queries that ask whether or not a subset of vertices contains an edge. We study the non-adaptive model…
The minimum-cost subset $k$-connected subgraph problem is a cornerstone problem in the area of network design with vertex connectivity requirements. In this problem, we are given a graph $G=(V,E)$ with costs on edges and a set of terminals…
Minimum flow decomposition (MFD) is the NP-hard problem of finding a smallest decomposition of a network flow/circulation $X$ on a directed graph $G$ into weighted source-to-sink paths whose superposition equals $X$. We show that, for…
This paper considers the \textit{minimum spanning tree (MST)} problem in the Congested Clique model and presents an algorithm that runs in $O(\log \log \log n)$ rounds, with high probability. Prior to this, the fastest MST algorithm in this…
We revisit the deadline version of the discrete time-cost tradeoff problem for the special case of bounded depth. Such instances occur for example in VLSI design. The depth of an instance is the number of jobs in a longest chain and is…
We present practical linear and almost linear-time algorithms to compute a chain decomposition of a directed acyclic graph (DAG), $G=(V,E)$. The number of vertex-disjoint chains computed is very close to the minimum. The time complexity of…
In 2022, Chen et al. proposed an algorithm in \cite{main} that solves the min cost flow problem in $m^{1 + o(1)} \log U \log C$ time, where $m$ is the number of edges in the graph, $U$ is an upper bound on capacities and $C$ is an upper…
We investigate how the underlying graph of a network supports a flow between a source node and a destination node and propose to compute the expected number of nodes and links that contribute to transferring items in random graphs. Since…
The Directed Steiner Network (DSN) problem takes as input a directed edge-weighted graph $G=(V,E)$ and a set $\mathcal{D}\subseteq V\times V$ of $k$ demand pairs. The aim is to compute the cheapest network $N\subseteq G$ for which there is…
We show a deterministic algorithm for computing edge connectivity of a simple graph with $m$ edges in $m^{1+o(1)}$ time. Although the fastest deterministic algorithm by Henzinger, Rao, and Wang [SODA'17] has a faster running time of…