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We present the first non-trivial fully dynamic algorithm maintaining exact single-source distances in unweighted graphs. This resolves an open problem stated by Sankowski [COCOON 2005] and van den Brand and Nanongkai [FOCS 2019]. Previous…
Graph-searching algorithms play a crucial role in various computational domains, enabling efficient exploration and pathfinding in structured data. Traditional approaches, such as Depth-First Search (DFS) and Breadth-First Search (BFS),…
Random search methods are widely used for global optimization due to their theoretical generality and implementation simplicity. This paper proposes a depth-first directional search (DFDS) algorithm for globally solving nonconvex…
We consider the performance of the Depth First Search (DFS) algorithm on the random graph $G\left(n,\frac{1+\epsilon}{n}\right)$, $\epsilon>0$ a small constant. Recently, Enriquez, Faraud and M\'enard [2] proved that the stack $U$ of the…
Diffusion model deployment has been suffering from high energy consumption and inference latency despite its superior performance in visual generation tasks. Dynamic voltage and frequency scaling (DVFS) offers a promising solution to…
A (fully) dynamic graph algorithm is a data structure that supports edge insertions, edge deletions, and answers certain queries that are specific to the problem under consideration. There has been a lot of research on dynamic algorithms…
The maximum common subtree isomorphism problem asks for the largest possible isomorphism between subtrees of two given input trees. This problem is a natural restriction of the maximum common subgraph problem, which is ${\sf NP}$-hard in…
We consider the problem of compactly representing the Depth First Search (DFS) tree of a given undirected or directed graph having $n$ vertices and $m$ edges while supporting various DFS related queries efficiently in the RAM with…
As a fundamental topic in graph mining, Densest Subgraph Discovery (DSD) has found a wide spectrum of real applications. Several DSD algorithms, including exact and approximation algorithms, have been proposed in the literature. However,…
We study {\em breadth-first search (BFS)} spanning trees, and address the problem of designing a sparse {\em fault-tolerant} BFS structure, or {\em FT-BFS } for short, resilient to the failure of up to two edges in the given undirected…
Data-intensive, graph-based computations are pervasive in several scientific applications, and are known to to be quite challenging to implement on distributed memory systems. In this work, we explore the design space of parallel algorithms…
We present a work-efficient parallel level-synchronous Breadth First Search (BFS) algorithm for shared-memory architectures which achieves the theoretical lower bound on parallel running time. The optimality holds regardless of the shape of…
While it is well-known and acknowledged that the performance of graph algorithms is heavily dependent on the input data, there has been surprisingly little research to quantify and predict the impact the graph structure has on performance.…
In this paper, we present a fully-dynamic distributed algorithm for maintaining a minimum spanning tree on general graphs with positive real edge weights. The goal of a dynamic MST algorithm is to update efficiently the minimum spanning…
It is well-known since the seventies of last century that Depth First Search (DFS) can be used to compute strongly connected components [RE. Tarjan. SIAM Journal on Computing, 1972] and Breadth First Search (BFS) can be used to compute…
We study the problem of maintaining a breadth-first spanning tree (BFS tree) in partially dynamic distributed networks modeling a sequence of either failures or additions of communication links (but not both). We present deterministic…
This study develops a graph search algorithm to find the optimal discrimination path for the binary classification problem. The objective function is defined as the difference of variations between the true positive (TP) and false positive…
Graph algorithms enormously contribute to the domains such as blockchains, social networks, biological networks, telecommunication networks, and several others. The ever-increasing demand of data-volume, as well as speed of such…
Highly dynamic networks are characterized by frequent changes in the availability of communication links. These networks are often partitioned into several components, which split and merge unpredictably. We present a distributed algorithm…
Depth first search is a natural algorithmic technique for constructing a closed route that visits all vertices of a graph. The length of such route equals, in an edge-weighted tree, twice the total weight of all edges of the tree and this…