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Kapunac, Stefan (Beograd , 2026)[more][less]
Abstract: This dissertation addresses methods for efficiently solving several important variants of domination problems on graphs, with a particular focus on large-scale instances that frequ- ently appear in real-world systems. Domination problems have numerous applications in the analysis and management of complex networks, including social, telecommunication, transport, and biological networks. The study covers four problems: minimum weight total domination, minimum weight independent domination, k-strong Roman domination, and the canonical mi- nimum domination problem on large graphs. For the minimum weight total domination problem, a variable neighborhood search approach is proposed, with carefully designed mechanisms for shaking, local search, and fitness function evaluation. The results show that the proposed algorithm achieves optimal solutions on small and medium instances and outperforms competing approaches on large graphs. Additionally, an application of this problem for accelerating information spreading in social networks is proposed. For the minimum weight independent domination problem, two new integer linear pro- gramming models are developed. Solving these models finds optimal solutions for all smaller instances while demonstrating superior performance compared to competing exact approaches on larger graphs. In addition, a greedy heuristic is proposed that outperforms competing greedy methods on most instances. In the case of k-strong Roman domination, a greedy heuristic based on node coverage information is developed, along with a metaheuristic approach based on variable neighborhood search that uses the greedy algorithm for initialization. This problem is particularly challenging due to the exponential complexity of solution feasibility verification, leading to the introduction of the concept of quasi-feasibility that enables efficient feasibility assessment during the search. Experimental results show that the proposed algorithm consistently outperforms the greedy approach and existing competing methods, especially on larger graphs. The practical value of the algorithm is illustrated through a case study involving the optimal positioning of fire stations and vehicles in urban municipalities to ensure the entire city is safe in the event of k simultaneous fires. For the minimum domination problem, a new hybrid approach called IRIS is proposed. IRIS is designed as a general-purpose framework that bridges the gap between exact integer linear programming solvers and heuristic search by iteratively fixing selected variables to reduce the search space. Тhe novelty lies in its flexible subproblem construction mechanism, which can be tailored using various selection strategies. In this study, we implement and evaluate a specific configuration of IRIS that utilizes historical statistical data and a node-coverage-based heuristic to intelligently identify variables for fixing. This targeted approach allows the ILP solver to find high-quality solutions for large-scale instances that are computationally prohibitive for exact methods. Experimental results demonstrate that IRIS achieves competitive performance com- pared to the best existing methods, establishing it as a valid alternative for solving domination and potentially other NP-hard problems. URI: http://hdl.handle.net/123456789/5782 Files in this item: 1
phdStefanKapunac.pdf ( 3.299Mb ) -
Aleksić, Danijel (Beograd , 2026)[more][less]
Abstract: This dissertation addresses the problem of model specification testing in situa- tions where data are incomplete, utilizing the existing theory of non-degenerate and weakly degenerate U- and V-statistics. The first two chapters lay the theoretical groundwork by pre- senting essential concepts related to U- and V-statistics and the general mathematical frame- work of missing data analysis, which serve as the foundation for the new results developed in subsequent chapters. In Chapter 3, a novel test for assessing the missing completely at random (MCAR) assump- tion is introduced. This test demonstrates improved control of the type I error rate and supe- rior power performance compared to the main competitor across the majority of the simulated scenarios examined. Chapter 4 explores the application of Kendall’s test for independence in the presence of MCAR data. It provides both theoretical insights and simulation-based comparisons of the complete-case analysis and median imputation, pointing out their individual advantages and drawbacks. Chapter 5 focuses on testing for multivariate normality when data are incomplete. It rig- orously establishes the validity of the complete-case approach under MCAR and proposes a bootstrap method to approximate p -values when imputation is employed. Additionally, vari- ous imputation techniques are evaluated with respect to their impact on the type I error and the power of the test. Finally, Chapter 6 adapts the energy-based two-sample test to handle missing data by intro- ducing a weighted framework that makes full use of all available observations. Alongside some theoretical developments, the chapter presents two distinct bootstrap algorithms for p -value estimation under this approach. Additionally, the performance of several imputation methods is examined in this context, and appropriate bootstrap algorithm is proposed for that setting. URI: http://hdl.handle.net/123456789/5781 Files in this item: 1
DanijelAleksicPhDThesis.pdf ( 4.605Mb ) -
Bogdanović, Katarina (Beograd , 2025)[more][less]
Abstract: In the rst and the second chapter of dissertation we prove some new inequalities for the spectral radius, essential spectral radius, oper- ator norm, measure of non-compactness and numerical radius of Hadamard (Schur) weighted geometric means of positive kernel operators on Banach function and sequence spaces. The list of extensions and re nings of known inequalities has been expanded. Some new inequalities and equalities for the generalized and the joint spectral radius and their essential versions of Hadamard (Schur) geometric means of bounded sets of positive kernel op- erators on Banach function spaces have been proved. There are additional results in case of non-negative matrices that de ne operators on Banach sequence spaces. In the third part we present some inequalities for opera- tor monotone functions and (co)hyponormal operators and give relations of Schur multipliers to derivation like inequalities for operators. In particular, let Ψ, Φ be s.n. functions, p ⩾ 2 and φ be an operator monotone function on [0, ∞) such that φ(0) = 0. If A, B, X ∈ B(H) and A and B are strictly ac- cretive such that AX−XB ∈ CΨ(H), then also AXφ(B)−φ(A)XB ∈ CΨ(H) and ||AXφ(B) − φ(A)XB||Ψ ⩽ r φ A+A∗ 2 − A+A∗ 2 φ′ A+A∗ 2 A+A∗ 2 −1 A(AX − XB)B B+B∗ 2 −1 r φ B+B∗ 2 − B+B∗ 2 φ′ B+B∗ 2 Ψ . under any of the following conditions: (a) Both A and B are normal, (b) A is cohyponormal, B is hyponormal and at least one of them is normal, and Ψ := Φ(p)∗ , (c) A is cohyponormal, B is hyponormal and ||.||Ψ is the trace norm ||.||1. Alternative inequalities for ||.||Ψ(p) norms are also obtained. URI: http://hdl.handle.net/123456789/5780 Files in this item: 1
Katarina_Bogdanovic_disertacija.pdf ( 1.621Mb ) -
Krstić, Mihailo (Beograd , 2025)[more][less]
Abstract: This doctoral dissertation addresses the integration of functions taking values in spaces of bounded operators and in spaces of complex measures on a given σ-algebra. The mentioned integrability is considered in a more general sense than that required in the theory of weak integration of vector-valued functions. The first part of the dissertation deals with the integrability of families of operators. If (Ω, M, μ) is a space with a positive measure μ and (At)t∈Ω is a family of operators from B(X, Y ), where X and Y are Banach spaces, then μ-integrability of the function Ω ∋ t 7 → ⟨Atx, y∗⟩ ∈ C is required for every x ∈ X and y∗ ∈ Y ∗. In this case, we prove that the quantity sup∥x∥=∥y∗∥=1 R Ω ⟨Atx, y∗⟩ dμ(t) is finite. This expres- sion allows us to define a norm on the corresponding vector space of families of operators. Furthermore, for every E ∈ M, one obtains an operator R E At dμ(t) in B(X, Y ∗∗), whose defining property is ⟨y∗, R E At dμ(t) x⟩ = R E ⟨Atx, y∗⟩ dμ(t) for every x ∈ X and y∗ ∈ Y ∗. The second part of the dissertation deals with the integrability of families of measures. If (λx)x∈X is a family of complex measures on (Y, A), where (X, B, μ) is a space with a positive measure μ, and if for every A ∈ A the function X ∋ x 7 → λx(A) ∈ C is μ-integrable, then the quantity supA∈A R X |λx(A)| dμ(x) is finite. This allows us to define a norm on the corresponding vector space of families of measures. In this case, for every B ∈ B there exists a complex measure R B λx dμ(x) on A such that R B λx dμ(x) (A) = R B λx(A) dμ(x) for every A ∈ A. The dis- sertation is organized as follows. The first part (Chapters 2–4) deals with the integration of functions taking values in B(X, Y ). Chapter 2 provides a survey of the known results on the integration of functions in B(H), where H is a separable Hilbert space, and presents original results extending the existing theory. In Chapter 3, the developed theory is applied to the Laplace transform of B(H)-valued functions, which has been previously considered in the literature. Chapter 4 is significant because it generalizes the integrability of functions taking values in B(X, Y ). This type of integration was first defined in [8]. The second part of the dissertation (Chapter 5) deals with the integration of functions taking values in spaces of complex measures on a given σ-algebra. The introduced type of integration is more general than Pettis concept and has been considered in [6, 7]. These works represent a natural ex- tension and application of the experiences gained from working with functions taking values in operator spaces, including original results of the candidate with coauthors. Numerous concrete examples are included, making this abstract material much more illustrative. URI: http://hdl.handle.net/123456789/5779 Files in this item: 1
Disertacija_M_Krstic.pdf ( 3.184Mb ) -
Čugurović, Milan (Beograd , 2025)[more][less]
Abstract: Compilers use program profiles to perform profile-guided optimizations and pro- duce efficient programs. Although dynamic profilers generate high-quality profiles, they have significant drawbacks. They complicate the application build pipeline by requiring two compi- lation steps and an additional profile collection run. Dynamic profilers also consume substantial time and memory and place a heavy burden on developers to create suitable workloads that accurately reflect typical application usage, cover important code paths, and generate well- distributed profiles. In response to the shortcomings of dynamic profilers, modern static profilers employ ma- chine learning (ML) techniques to predict program profiles. However, state-of-the-art ML-based static profilers often rely on handcrafted features that are platform-specific and difficult to adapt across different architectures and programming languages. They also tend to use computation- ally intensive deep neural networks, which increase application compilation time. Moreover, ML-based static profilers can degrade the performance of optimized programs due to inaccurate profile predictions. This dissertation presents GraalSP , an ML-based static profiler that is portable, polyglot, efficient, and robust. GraalSP achieves portability by defining features on a high-level, graph- based intermediate representation and by partially automating the feature extraction process. This design makes GraalSP polyglot, allowing it to predict profiles for programs written in any language that compiles to Java bytecode, such as Java, Scala, or Kotlin. GraalSP is efficient due to its use of a lightweight XGBoost model based on decision trees, and robust because it relies on carefully designed heuristics that correct machine learning predictions and ensure high performance in programs optimized using the predicted profiles. We integrate GraalSP into the Enterprise GraalVM Native Image compiler and evaluate it on 28 benchmarks from the Renaissance, DaCapo, and DaCapo Scala benchmark suites. These suites represent a modern and diverse collection of benchmarks, featuring numerous real-world workloads across a variety of programming paradigms. Our comprehensive evaluation shows that GraalSP achieves a geometric mean speedup of 7.46% in execution time compared to the default compiler configuration, which models program profiles using a uniform distribution. This dissertation also presents a detailed qualitative and quantitative analysis to position and compare the proposed solution against state-of-the-art static profilers. Additionally, to enhance and expand the evaluation and support developers in analyzing GraalSP ’s predictions, this dissertation introduces the GraalSP-PLog tool. This tool allows developers to run the GraalSP static profiler on any program and generate detailed prediction reports, making it easier to inspect individual predictions and identify model mispredictions. Since GraalSP provides substantial performance gains, has minimal impact on binary size and compile time, and includes a modern, fully automated model retraining pipeline, it is well- suited for commercial deployment. As a result, GraalSP has been the default static profiler for the Enterprise GraalVM Native Image compiler since June 2023, consistently improving performance with every build. URI: http://hdl.handle.net/123456789/5778 Files in this item: 1
Milan_Cugurovic_doktorska_disertacija.pdf ( 5.694Mb )