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Let G=(V,E) be a graph with f:V\to Z_+ a function assigning degree bounds to vertices. We present the first efficient algebraic algorithm to find an f-factor. The time is \tilde{O}(f(V)^{\omega}). More generally for graphs with integral…
The Steiner tree problem aims to determine a minimum edge-weighted tree that spans a given set of terminal vertices from a given graph. In the past decade, a considerable number of algorithms have been developed to solve this…
Processing graphs with temporal information (the temporal graphs) has become increasingly important in the real world. In this paper, we study efficient solutions to temporal graph applications using new algorithms for Incremental Minimum…
Min-Cut queries are fundamental: Preprocess an undirected edge-weighted graph, to quickly report a minimum-weight cut that separates a query pair of nodes $s,t$. The best data structure known for this problem simply builds a cut-equivalent…
Given an edge-weighted graph $G=(V,E)$ and a set $E_0\subset E$, the incremental network design problem with minimum spanning trees asks for a sequence of edges $e'_1,\ldots,e'_T\in E\setminus E_0$ minimizing $\sum_{t=1}^Tw(X_t)$ where…
Given a spatio-temporal network (ST network) where edge properties vary with time, a time-sub-interval minimum spanning tree (TSMST) is a collection of minimum spanning trees of the ST network, where each tree is associated with a time…
Given an undirected, weighted graph, the minimum spanning tree (MST) is a tree that connects all of the vertices of the graph with minimum sum of edge weights. In real world applications, network designers often seek to quickly find a…
The minimum-cost arborescence problem is a well-studied problem in the area of graph theory, with known polynomial-time algorithms for solving it. Previous literature introduced new variations on the original problem with different…
Finding shortest paths in a graph is relevant for numerous problems in computer vision and graphics, including image segmentation, shape matching, or the computation of geodesic distances on discrete surfaces. Traditionally, the concept of…
We present a new fast all-pairs shortest path algorithm for unweighted graphs. In breadth-first search which is said to representative and fast in unweighted graphs, the average number of accesses to adjacent vertices (expressed by…
In a temporal graph, each edge is available at specific points in time. Such an availability point is often represented by a ''temporal edge'' that can be traversed from its tail only at a specific departure time, for arriving in its head…
Compact and I/O-efficient data representations play an important role in efficient algorithm design, as memory bandwidth and latency can present a significant performance bottleneck, slowing the computation by orders of magnitude. While…
While the shortest path problem has myriad applications, the computational efficiency of suitable algorithms depends intimately on the underlying problem domain. In this paper, we focus on domains where evaluating the edge weight function…
Minimum Spanning Tree (MST) is an important graph algorithm that has wide ranging applications in the areas of computer networks, VLSI routing, wireless communications among others. Today virtually every computer is built out of multi-core…
Many discrete optimization problems amount to selecting a feasible set of edges of least weight. We consider in this paper the context of spatial graphs where the positions of the vertices are uncertain and belong to known uncertainty sets.…
The shortest paths problem is a fundamental challenge in graph theory, with a broad range of potential applications. The algorithms based on matrix multiplication exhibits excellent parallelism and scalability, but is constrained by high…
In this paper, we study weakly dynamic undirected graphs, that can be used to represent some logistic networks. The goal is to deliver all the delivery points in the network. The network exists in a mostly stable environment, except for a…
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 study the {\em min-cost chain-constrained spanning-tree} (abbreviated \mcst) problem: find a min-cost spanning tree in a graph subject to degree constraints on a nested family of node sets. We devise the {\em first} polytime algorithm…
The run time complexity of state-of-the-art inference algorithms in graph-based dependency parsing is super-linear in the number of input words (n). Recently, pruning algorithms for these models have shown to cut a large portion of the…