arXiv subjects

Evangelos Bampas

Publications and source records attributed to Evangelos Bampas.

4 recordsLinked to original sources

arXiv2026

Emergency Vertex Cover

The Minimum Vertex Cover problem is a fundamental combinatorial optimization problem, aiming to identify a minimum subset of vertices in a graph such that every edge is incident to at least one vertex in this subset. Among its variants, the Min-Power-Cover problem stands out due to its practical applications, such as camera placement at intersections: in an edge-weighted graph, an edge is covered if one of its endpoints is assigned a power value at least as large as the edge's weight. In this paper, we introduce the Emergency Vertex Cover (Em-VC) problem where an edge may be covered not only by its endpoints, but also by a distant vertex, provided the vertex is given sufficient power to "cover" the cumulative weight of the edges along a shortest path to one of the edge's endpoints plus the weight of the edge. Em-VC is motivated by different practical scenarios, e.g. the need for urban disaster response, where ensuring accessibility to all road segments (edges of the graph) is crucial for effective aid delivery. We prove that Em-VC is NP-hard, derive lower bounds, and design a polynomial-time algorithm for its continuous version. Moreover, we present a 4/3-approximation algorithm for the discrete case and identify several special graph classes for which the problem can be solved in polynomial time.

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arXiv2025

Perpetual exploration in anonymous synchronous networks with a Byzantine black hole

In this paper, we investigate: ``How can a group of initially co-located mobile agents perpetually explore an unknown graph, when one stationary node occasionally behaves maliciously, under an adversary's control?'' We call this node a ``Byzantine black hole (BBH)'' and at any given round it may choose to destroy all visiting agents, or none. This subtle power can drastically undermine classical exploration strategies designed for an always active black hole. We study this perpetual exploration problem in the presence of at most one BBH, without initial knowledge of the network size. Since the underlying graph may be 1-connected, perpetual exploration of the entire graph may be infeasible. We thus define two variants: \pbmPerpExpl\ and \pbmPerpExplHome. In the former, the agents are tasked to perform perpetual exploration of at least one component, obtained after the exclusion of the BBH. In the latter, the agents are tasked to perform perpetual exploration of the component which contains the \emph{home} node, where agents are initially co-located. Naturally, \pbmPerpExplHome\ is a special case of \pbmPerpExpl. Agents operate under a synchronous scheduler and communicate in a face-to-face model. Our goal is to determine the minimum number of agents necessary and sufficient to solve these problems. In acyclic networks, we obtain optimal algorithms that solve \pbmPerpExpl\ with $4$ agents, and \pbmPerpExplHome\ with $6$ agents in trees. The lower bounds hold even in path graphs. In general graphs, we give a non-trivial lower bound of $2Δ-1$ agents for \pbmPerpExpl, and an upper bound of $3Δ+3$ agents for \pbmPerpExplHome. To our knowledge, this is the first study of a black-hole variant in arbitrary networks without initial topological knowledge.

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arXiv2018

Maximal Exploration of Trees with Energy-Constrained Agents

We consider the problem of exploring an unknown tree with a team of $k$ initially colocated mobile agents. Each agent has limited energy and cannot, as a result, traverse more than $B$ edges. The goal is to maximize the number of nodes collectively visited by all agents during the execution. Initially, the agents have no knowledge about the structure of the tree, but they gradually discover the topology as they traverse new edges. We assume that the agents can communicate with each other at arbitrary distances. Therefore the knowledge obtained by one agent after traversing an edge is instantaneously transmitted to the other agents. We propose an algorithm that divides the tree into subtrees during the exploration process and makes a careful trade-off between breadth-first and depth-first exploration. We show that our algorithm is 3-competitive compared to an optimal solution that we could obtain if we knew the map of the tree in advance. While it is easy to see that no algorithm can be better than 2-competitive, we give a non-trivial lower bound of 2.17 on the competitive ratio of any online algorithm.

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arXiv2012

Self-Stabilizing Balancing Algorithm for Containment-Based Trees

Containment-based trees encompass various handy structures such as B+-trees, R-trees and M-trees. They are widely used to build data indexes, range-queryable overlays, publish/subscribe systems both in centralized and distributed contexts. In addition to their versatility, their balanced shape ensures an overall satisfactory performance. Re- cently, it has been shown that their distributed implementations can be fault-resilient. However, this robustness is achieved at the cost of un-balancing the structure. While the structure remains correct in terms of searchability, its performance can be significantly decreased. In this paper, we propose a distributed self-stabilizing algorithm to balance containment-based trees.

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