TY - GEN
T1 - Black Hole Search by Scattered Agents on Time-Varying Dynamic Graphs
AU - Kaur, Tanvir
AU - Saxena, Ashish
AU - Mandal, Partha Sarathi
AU - Mondal, Kaushik
N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2026.
PY - 2026/1/1
Y1 - 2026/1/1
N2 - A black hole is a malicious node in a graph that destroys resources entering into it without leaving any trace. The problem of Black Hole Search (BHS) using mobile agents requires that at least one agent survive and terminate after locating the black hole. Recently, this problem is studied on 1-bounded 1-interval connected dynamic graphs, where there is a footprint graph, and at most one edge can disappear from the footprint in a round, provided that the graph remains connected. In this setting, the authors proposed an algorithm that solves the BHS problem when all agents start from a single node (rooted initial configuration). They also proved that at least 2δBH+1 agents are necessary to solve the problem when agents are initially placed arbitrarily across the nodes of the graph (scattered initial configuration), where δBH denotes the degree of the black hole. In this work, we present an algorithm that solves the BHS problem using 2δBH+17 many initially scattered agents. Our result matches asymptotically with the existing rooted algorithm under the same model assumptions.
AB - A black hole is a malicious node in a graph that destroys resources entering into it without leaving any trace. The problem of Black Hole Search (BHS) using mobile agents requires that at least one agent survive and terminate after locating the black hole. Recently, this problem is studied on 1-bounded 1-interval connected dynamic graphs, where there is a footprint graph, and at most one edge can disappear from the footprint in a round, provided that the graph remains connected. In this setting, the authors proposed an algorithm that solves the BHS problem when all agents start from a single node (rooted initial configuration). They also proved that at least 2δBH+1 agents are necessary to solve the problem when agents are initially placed arbitrarily across the nodes of the graph (scattered initial configuration), where δBH denotes the degree of the black hole. In this work, we present an algorithm that solves the BHS problem using 2δBH+17 many initially scattered agents. Our result matches asymptotically with the existing rooted algorithm under the same model assumptions.
KW - Black Hole Search
KW - Deterministic Algorithms
KW - Distributed Algorithms
KW - Dynamic Graphs
KW - Mobile Agents
KW - Time-Varying Graphs
UR - https://www.scopus.com/pages/publications/105023147888
U2 - 10.1007/978-3-032-11127-2_25
DO - 10.1007/978-3-032-11127-2_25
M3 - Conference contribution
AN - SCOPUS:105023147888
SN - 9783032111265
T3 - Lecture Notes in Computer Science
SP - 309
EP - 324
BT - Stabilization, Safety, and Security of Distributed Systems - 27th International Symposium, SSS 2025, Proceedings
A2 - Bonomi, Silvia
A2 - Mandal, Partha Sarathi
A2 - Robinson, Peter
A2 - Sharma, Gokarna
A2 - Tixeuil, Sebastien
PB - Springer Science and Business Media Deutschland GmbH
T2 - 27th International Symposium on Stabilization, Safety, and Security of Distributed Systems, SSS2025
Y2 - 9 October 2025 through 11 October 2025
ER -