Related papers: Optimal In-place Algorithms for Basic Graph Proble…
A graph is $k$-degenerate if any induced subgraph has a vertex of degree at most $k$. In this paper we prove new algorithms for cliques and similar structures for these graphs. We design linear time Fixed-Parameter Tractable algorithms for…
Given an input $x$, and a search problem $F$, local computation algorithms (LCAs) implement access to specified locations of $y$ in a legal output $y \in F(x)$, using polylogarithmic time and space. Mansour et al., (2012), had previously…
A dynamic graph algorithm is a data structure that answers queries about a property of the current graph while supporting graph modifications such as edge insertions and deletions. Prior work has shown strong conditional lower bounds for…
Reducing the running time of graph algorithms is vital for tackling real-world problems such as shortest paths and matching in large-scale graphs, where path information plays a crucial role. To address this critical challenge, this paper…
We study the classical scheduling problem on parallel machines %with precedence constraints where the precedence graph has the bounded depth $h$. Our goal is to minimize the maximum completion time. We focus on developing approximation…
Visual place recognition is an important subproblem of mobile robot localization. Since it is a special case of image retrieval, the basic source of information is the pairwise similarity of image descriptors. However, the embedding of the…
We consider the problem of finding \textit{semi-matching} in bipartite graphs which is also extensively studied under various names in the scheduling literature. We give faster algorithms for both weighted and unweighted case. For the…
Graphs naturally appear in several real-world contexts including social networks, the web network, and telecommunication networks. While the analysis and the understanding of graph structures have been a central area of study in algorithm…
Computing paths in graph structures is a fundamental operation in a wide range of applications, from transportation networks to data analysis. The beer path problem, which captures the option of visiting points of interest, such as gas…
In the classical facility location problem we consider a graph $G$ with fixed weights on the edges of $G$. The goal is then to find an optimal positioning for a set of facilities on the graph with respect to some objective function. We…
Graph partitioning schedules parallel calculations like sparse matrix-vector multiply (SpMV). We consider contiguous partitions, where the $m$ rows (or columns) of a sparse matrix with $N$ nonzeros are split into $K$ parts without…
Let $P$ be a path graph of $n$ vertices embedded in a metric space. We consider the problem of adding a new edge to $P$ so that the radius of the resulting graph is minimized, where any center is constrained to be one of the vertices of…
We initiate the study of a fundamental combinatorial problem: Given a capacitated graph $G=(V,E)$, find a shortest walk ("route") from a source $s\in V$ to a destination $t\in V$ that includes all vertices specified by a set…
A dynamic graph algorithm is a data structure that supports edge insertions, deletions, and specific problem queries. While extensive research exists on dynamic algorithms for graph problems solvable in polynomial time, most of these…
Finding optimal matchings in dense graphs is of general interest and of particular importance in social, transportation and biological networks. While developing optimal solutions for various matching problems is important, the running…
Graph partition is a key component to achieve workload balance and reduce job completion time in parallel graph processing systems. Among the various partition strategies, edge partition has demonstrated more promising performance in…
Graph planning gives rise to fundamental algorithmic questions such as shortest path, traveling salesman problem, etc. A classical problem in discrete planning is to consider a weighted graph and construct a path that maximizes the sum of…
Optimal linear-time algorithms for testing the planarity of a graph are well-known for over 35 years. However, these algorithms are quite involved and recent publications still try to give simpler linear-time tests. We give a simple…
We study the problem of finding the cycle of minimum cost-to-time ratio in a directed graph with $ n $ nodes and $ m $ edges. This problem has a long history in combinatorial optimization and has recently seen interesting applications in…
A graph $G$ is said to be a $(k,\ell)$-graph if its vertex set can be partitioned into $k$ independent sets and $\ell$ cliques. It is well established that the recognition problem for $(k,\ell)$-graphs is NP-complete whenever $k \geq 3$ or…