arXiv subjects

Hovhannes A. Harutyunyan

Publications and source records attributed to Hovhannes A. Harutyunyan.

5 recordsLinked to original sources

arXiv2026

A Linear-Time 1.5-Approximation for Broadcasting in k-Cycle Graphs

Broadcasting is an information dissemination primitive where a message originates at a node (called the originator) and is passed to all other nodes in the network. Broadcasting research is motivated by efficient network design and determining the broadcast times of standard network topologies. Verifying the broadcast time of a node $v$ in an arbitrary network $G$ is known to be NP-hard. Additionally, recent findings show that the broadcast time problem is NP-hard in several highly restricted subfamilies of cactus graphs. The most restrictive of these families is known as \emph{$k$-cycle graphs} or \emph{flower graphs} and is the focus of this paper. We present a simple $(1.5-ε)$-approximation algorithm for determining the broadcast time of networks modeled using $k$-cycle graphs, where $ε> 0$ depends on the structure of the graph.

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arXiv2026

On Hardness and Approximation of Broadcasting in Structured Graphs

We study the Telephone Broadcasting problem in graphs with restricted structure. Given a designated source in an undirected graph, the goal is to disseminate a message to all vertices in the minimum number of rounds, where in each round every informed vertex may inform at most one neighbor. For general graphs, the problem is NP-hard. Recent work shows that the problem remains NP-hard even on restricted graph classes such as graphs of treewidth 2 [Tale 2025], cactus graphs of pathwidth 2 [Aminian et~al. 2025] and graphs at distance 1 to a path forest [Egami et~al. 2025]. In this work, we investigate the problem in several graph families. We first prove NP-hardness for cycle-star graphs, graphs formed by k cycles sharing a single vertex, as well as melon graphs, graphs formed by k paths with shared endpoints. Despite multiple efforts to understand the problem in these simple graph families, the computational complexity of the problem remained unsettled. Our hardness results answer open questions by Bhabak and Harutyunyan [2015] and Harutyunyan and Hovhannisyan [2023] concerning the problem's complexity in cycle-star and melon graphs, respectively. On the positive side, we present EPTASs for cycle-star and melon graphs, improving over the best existing approximation factors of 2 for both graph families. Moreover, we identify a structural frontier for tractability by showing that the problem is solvable in polynomial time on graphs of bounded cutwidth, a class that generalizes other families such as graphs of bounded bandwidth. This result subsumes existing tractability results for graph families such as necklace graphs. Finally, for split graphs, a fundamental class of highly structured graphs, we obtain a polynomial-time algorithm with approximation factor 1.76. This improves on the previously known factor 2 bound; the same approach also applies to the multi-source setting.

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arXiv2026

Series-Parallel and Planar Graphs for Efficient Broadcasting

The broadcasting problem concerns the efficient dissemination of information in graphs. In classical broadcasting, a single originator vertex initially has a message to be transmitted to all vertices. Every vertex which has received the message informs at most one uninformed neighbor at each discrete time unit. In this paper, we introduce infinite families of series-parallel graphs with efficient broadcast times: graphs on $n$ vertices with broadcast time at most $\lceil\log_2 n \rceil + 1$ for any $n$, graphs on $n$ vertices with broadcast time $\lfloor \frac{3 \lceil \log_2 n \rceil}{2} \rfloor$ and maximum degree $\lceil \log_2 n \rceil - 1$ for any $n$, and broadcast graphs on up to $2^{k-1} + 2^{\lfloor \frac{k}{2} \rfloor }$ vertices with broadcast time $k$ for any $k$. We also introduce an infinite family of planar broadcast graphs on up to $2^{k-1} + 2^{\lfloor \frac{3k}{4} \rfloor - 1}$ vertices with broadcast time $k$ for any $k$, which improves the known lower bound on the maximum number of vertices in a planar broadcast graph.

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arXiv2025

Source-Oblivious Broadcast

This paper revisits the study of (minimum) broadcast graphs, i.e., graphs enabling fast information dissemination from every source node to all the other nodes (and having minimum number of edges for this property). This study is performed in the framework of compact distributed data structures, that is, when the broadcast protocols are bounded to be encoded at each node as an ordered list of neighbors specifying, upon reception of a message, in which order this message must be passed to these neighbors. We show that this constraint does not limit the power of broadcast protocols, as far as the design of (minimum) broadcast graphs is concerned. Specifically, we show that, for every~$n$, there are $n$-node graphs for which it is possible to design protocols encoded by lists yet enabling broadcast in $\lceil\log_2n\rceil$ rounds from every source, which is optimal even for general (i.e., non space-constrained) broadcast protocols. Moreover, we show that, for every~$n$, there exist such graphs with the additional property that they are asymptotically as sparse as the sparsest graphs for which $\lceil\log_2n\rceil$-round broadcast protocols exist, up to a constant multiplicative factor. Concretely, these graphs have $O(n\cdot L(n))$ edges, where $L(n)$ is the number of leading~1s in the binary representation of $n-1$, and general minimum broadcast graphs are known to have $Ω(n\cdot L(n))$ edges.

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arXiv2023

Temporal Separators with Deadlines

We study temporal analogues of the Unrestricted Vertex Separator problem from the static world. An $(s,z)$-temporal separator is a set of vertices whose removal disconnects vertex $s$ from vertex $z$ for every time step in a temporal graph. The $(s,z)$-Temporal Separator problem asks to find the minimum size of an $(s,z)$-temporal separator for the given temporal graph. We introduce a generalization of this problem called the $(s,z,t)$-Temporal Separator problem, where the goal is to find a smallest subset of vertices whose removal eliminates all temporal paths from $s$ to $z$ which take less than $t$ time steps. Let $τ$ denote the number of time steps over which the temporal graph is defined (we consider discrete time steps). We characterize the set of parameters $τ$ and $t$ when the problem is $\mathcal{NP}$-hard and when it is polynomial time solvable. Then we present a $τ$-approximation algorithm for the $(s,z)$-Temporal Separator problem and convert it to a $τ^2$-approximation algorithm for the $(s,z,t)$-Temporal Separator problem. We also present an inapproximability lower bound of $Ω(\ln(n) + \ln(τ))$ for the $(s,z,t)$-Temporal Separator problem assuming that $\mathcal{NP}\not\subset\mbox{\sc Dtime}(n^{\log\log n})$. Then we consider three special families of graphs: (1) graphs of branchwidth at most $2$, (2) graphs $G$ such that the removal of $s$ and $z$ leaves a tree, and (3) graphs of bounded pathwidth. We present polynomial-time algorithms to find a minimum $(s,z,t)$-temporal separator for (1) and (2). As for (3), we show a polynomial-time reduction from the Discrete Segment Covering problem with bounded-length segments to the $(s,z,t)$-Temporal Separator problem where the temporal graph has bounded pathwidth.

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