Related papers: Some Extensions of the All Pairs Bottleneck Paths …
We present a very simple and intuitive algorithm to find balanced sparse cuts in a graph via shortest-paths. Our algorithm combines a new multiplicative-weights framework for solving unit-weight multi-commodity flows with standard ball…
We construct a family of planar graphs $\{G_n\}_{n\geq 4}$, where $G_n$ has $n$ vertices including a source vertex $s$ and a sink vertex $t$, and edge weights that change linearly with a parameter $\lambda$ such that, as $\lambda$ varies in…
In the semi-streaming model, an algorithm must process any $n$-vertex graph by making one or few passes over a stream of its edges, use $O(n \cdot \text{polylog }n)$ words of space, and at the end of the last pass, output a solution to the…
We study the problem of computing shortest paths in so-called dense distance graphs. Every planar graph $G$ on $n$ vertices can be partitioned into a set of $O(n/r)$ edge-disjoint regions (called an $r$-division) with $O(r)$ vertices each,…
The disjoint paths problem is a fundamental problem in algorithmic graph theory and combinatorial optimization. For a given graph $G$ and a set of $k$ pairs of terminals in $G$, it asks for the existence of $k$ vertex-disjoint paths…
We study ROUND-UFP and ROUND-SAP, two generalizations of the classical BIN PACKING problem that correspond to the unsplittable flow problem on a path (UFP) and the storage allocation problem (SAP), respectively. We are given a path with…
In this paper, we study bottleneck identification in networks via extracting minimax paths. Many real-world networks have stochastic weights for which full knowledge is not available in advance. Therefore, we model this task as a…
The shortest secure path (routing) problem in communication networks has to deal with multiple attack layers e.g., man-in-the-middle, eavesdropping, packet injection, packet insertion, etc. Consider different probabilities for each such…
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…
Matrix $M$ is {\em $k$-concise} if the finite entries of each column of $M$ consist of $k$ or less intervals of identical numbers. We give an $O(n+m)$-time algorithm to compute the row minima of any $O(1)$-concise $n\times m$ matrix. Our…
Let $P$ be a path graph of $n$ vertices embedded in a metric space. We consider the problem of adding a new edge to $P$ to minimize the radius of the resulting graph. Previously, a similar problem for minimizing the diameter of the graph…
We consider the problem of finding maximum flows in planar graphs with capacities on both vertices and edges and with multiple sources and sinks. We present three algorithms when the capacities are integers. The first algorithm runs in $O(n…
A signed tree model of a graph $G$ is a compact binary structure consisting of a rooted binary tree whose leaves are bijectively mapped to the vertices of $G$, together with 2-colored edges $xy$, called transversal pairs, interpreted as…
In this paper we present an $\tilde{O}(m\sqrt{n}\log^{O(1)}U)$ time algorithm for solving the maximum flow problem on directed graphs with $m$ edges, $n$ vertices, and capacity ratio $U$. This improves upon the previous fastest running time…
Study the general single-source shortest path problem. Firstly, define a path function on a set of some path with same source on a graph, and develop a kind of general single-source shortest path problem (GSSSP) on the defined path…
Given an undirected $n$-vertex graph and $k$ pairs of terminal vertices $(s_1,t_1), \ldots, (s_k,t_k)$, the $k$-Disjoint Shortest Paths ($k$-DSP)-problem asks whether there are $k$ pairwise vertex-disjoint paths $P_1,\ldots, P_k$ such that…
We show that the following variation of the single-source shortest path problem is NP-complete. Let a weighted, directed, acyclic graph $G=(V,E,w)$ with source and sink vertices $s$ and $t$ be given. Let in addition a mapping $f$ on $E$ be…
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…
In this work we address a game theoretic variant of the shortest path problem, in which two decision makers (players) move together along the edges of a graph from a given starting vertex to a given destination. The two players take turns…
We study the design of fixed-parameter algorithms for problems already known to be solvable in polynomial time. The main motivation is to get more efficient algorithms for problems with unattractive polynomial running times. Here, we focus…