Related papers: Interval Routing Schemes for Circular-Arc Graphs
A graph is concave-round if its vertices can be circularly enumerated so that the closed neighbourhood of each vertex is an interval in the enumeration. In this work, we give a minimal forbidden induced subgraph characterization for the…
Reconfiguring two shortest paths in a graph means modifying one shortest path to the other by changing one vertex at a time so that all the intermediate paths are also shortest paths. This problem has several natural applications, namely:…
We consider the problem of computing routing schemes in the $\mathsf{HYBRID}$ model of distributed computing where nodes have access to two fundamentally different communication modes. In this problem nodes have to compute small labels and…
Path planning is a fundamental problem in road networks, with the goal of finding a path that optimizes objectives such as shortest distance or minimal travel time. Existing methods typically use graph indexing to ensure the efficiency of…
An interval graph is the intersection graph of a finite set of intervals on a line and a circular-arc graph is the intersection graph of a finite set of arcs on a circle. While a forbidden induced subgraph characterization of interval…
Realistic path planning applications often require optimizing with respect to several criteria simultaneously. Here we introduce an efficient algorithm for bi-criteria path planning on graphs. Our approach is based on augmenting the state…
The arc-routing problems are known to be notoriously hard. We study here a natural arc-routing problem on trees and more generally on bounded tree-width graphs and surprisingly show that it can be solved in a polynomial time. This implies a…
A proper edge-coloring of a graph is an interval coloring if the labels on the edges incident to any vertex form an interval of consecutive integers. Interval thickness s(G) of a graph G is the smallest number of interval colorable graphs…
McConnell [FOCS 2001] presented a flipping transformation from circular-arc graphs to interval graphs with certain patterns of representations. Beyond its algorithmic implications, this transformation is instrumental in identifying all…
We consider the standard message passing model; we assume the system is fully synchronous: all processes start at the same time and time proceeds in synchronised rounds. In each round each vertex can transmit a different message of size…
The betweenness centrality of a graph vertex measures how often this vertex is visited on shortest paths between other vertices of the graph. In the analysis of many real-world graphs or networks, betweenness centrality of a vertex is used…
An r-partite graph is an interval r-graph if corresponding to each vertex we can assign an interval of the real line such that two vertices u and v of different partite sets are adjacent if and only if their corresponding intervals…
In a graph whose vertices are assigned integer ranks, a path is well-ranked if the endpoints have distinct ranks or some interior point has a higher rank than the endpoints. A ranking is an assignment of ranks such that all nontrivial paths…
In the Minimum Clique Routing Problem on Cycles \textsc{MCRPC} we are given a cycle together with a set of demands (weighted origin-destination pairs) and the goal is to route all the pairs minimizing the maximum weighted clique of the…
We introduce the class of circular-arc H-graphs, which generalizes circular-arc graphs, particularly circular-arc bigraphs. We investigate two types of ordering-based characterizations of circular-arc r-graphs. Finally, we provide forbidden…
An interval $k$-graph is the intersection graph of a family $\mathcal{I}$ of intervals of the real line partitioned into at most $k$ classes with vertices adjacent if and only if their corresponding intervals intersect and belong to…
Vehicle routing algorithms usually reformulate the road network into a complete graph in which each arc represents the shortest path between two locations. Studies on time-dependent routing followed this model and therefore defined the…
Vertex splitting is a graph modification operation in which a vertex is replaced by multiple vertices such that the union of their neighborhoods equals the neighborhood of the original vertex. We introduce and study vertex splitting as a…
We propose bi-directional face traversal algorithm $2FACE$ to shorten the path the message takes to reach the destination in geometric routing. Our algorithm combines the practicality of the best single-direction traversal algorithms with…
In this work we consider temporal graphs, i.e. graphs, each edge of which is assigned a set of discrete time-labels drawn from a set of integers. The labels of an edge indicate the discrete moments in time at which the edge is available. We…