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Researcher profile

Morteza Saghafian

Morteza Saghafian contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
Computer Science and Game TheoryComputer VisionMachine Learningmath.CO

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Published work

3 published item(s)

preprint2026arXiv

CurveBench: A Benchmark for Exact Topological Reasoning over Nested Jordan Curves

We introduce CurveBench, a benchmark for hierarchical topological reasoning from visual input. CurveBench consists of \textbf{756 images} of pairwise non-intersecting Jordan curves across easy, polygonal, topographic-inspired, maze-like, and dense counting configurations. Each image is annotated with a rooted tree encoding the containment relations between planar regions. We formulate the task as structured prediction: given an image, a model must recover the full rooted containment tree induced by the curves. Despite the visual simplicity of the task, the strongest evaluated model, Gemini 3.1 Pro, achieves only \textbf{71.1\%} tree-generation accuracy on CurveBench-Easy and \textbf{19.1\%} on CurveBench-Hard. We further demonstrate benchmark utility through RLVR-style fine-tuning of open-weight vision-language models. Our trained Qwen3-VL-8B model improves over \texttt{Qwen-3-VL-8B-Thinking} from \textbf{2.8\%} to \textbf{33.3\%} tree-generation accuracy on CurveBench-Easy, exceeding GPT-5.4 and Claude Opus 4.5 under our evaluation protocol. The remaining gap, especially on CurveBench-Hard, shows that exact topology-aware visual reasoning remains far from solved.

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preprint2016arXiv

Improving the Bounds On Murty_Simon Conjecture

A graph is said to be diameter-$k$-critical if its diameter is $k$ and removal of any of its edges increases its diameter. A beautiful conjecture by Murty and Simon, says that every diameter-2-critical graph of order $n$ has at most $\lfloor n^2/4\rfloor$ edges and equality holds only for $K_{\lceil n/2 \rceil,\lfloor n/2 \rfloor }$. Haynes et al. proved that the conjecture is true for $Δ\geq 0.7n$. They also proved that for $n>2000$, if $Δ\geq 0.6789n$ then the conjecture is true. We will improve this bound by showing that the conjecture is true for every $n$ if $Δ\geq\ 0.676n$.

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preprint2012arXiv

On a Bounded Budget Network Creation Game

We consider a network creation game in which each player (vertex) has a fixed budget to establish links to other players. In our model, each link has unit price and each agent tries to minimize its cost, which is either its local diameter or its total distance to other players in the (undirected) underlying graph of the created network. Two versions of the game are studied: in the MAX version, the cost incurred to a vertex is the maximum distance between the vertex and other vertices, and in the SUM version, the cost incurred to a vertex is the sum of distances between the vertex and other vertices. We prove that in both versions pure Nash equilibria exist, but the problem of finding the best response of a vertex is NP-hard. We take the social cost of the created network to be its diameter, and next we study the maximum possible diameter of an equilibrium graph with n vertices in various cases. When the sum of players' budgets is n-1, the equilibrium graphs are always trees, and we prove that their maximum diameter is Theta(n) and Theta(log n) in MAX and SUM versions, respectively. When each vertex has unit budget (i.e. can establish link to just one vertex), the diameter of any equilibrium graph in either version is Theta(1). We give examples of equilibrium graphs in the MAX version, such that all vertices have positive budgets and yet the diameter is Omega(sqrt(log n)). This interesting (and perhaps counter-intuitive) result shows that increasing the budgets may increase the diameter of equilibrium graphs and hence deteriorate the network structure. Then we prove that every equilibrium graph in the SUM version has diameter 2^O(sqrt(log n)). Finally, we show that if the budget of each player is at least k, then every equilibrium graph in the SUM version is k-connected or has diameter smaller than 4.

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