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Department of Algorithms and Systems Modelling
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Catalog Publications
Year 2024
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Approximation algorithms for job scheduling with block-type conflict graphs
PublicationThe problem of scheduling jobs on parallel machines (identical, uniform, or unrelated), under incompatibility relation modeled as a block graph, under the makespan optimality criterion, is considered in this paper. No two jobs that are in the relation (equivalently in the same block) may be scheduled on the same machine in this model. The presented model stems from a well-established line of research combining scheduling theory...
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Deep Learning-Based, Multiclass Approach to Cancer Classification on Liquid Biopsy Data
PublicationThe field of cancer diagnostics has been revolutionized by liquid biopsies, which offer a bridge between laboratory research and clinical settings. These tests are less invasive than traditional biopsies and more convenient than routine imaging methods. Liquid biopsies allow studying of tumor-derived markers in bodily fluids, enabling the development of more precise cancer diagnostic tests for screening, disease monitoring, and...
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Equitable colorings of some variation of corona products of cubic graphs
PublicationThe problem of determining the value of equitable chromatic number for multicoronas of cubic graphs is studied. We provide some polynomially solvable cases of cubical multicoronas and give simple linear time algorithms for equitable coloring of such graphs which use almost optimal number of colors in the remaining cases.
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Potyczki algorytmiczne, czyli Alicja i Bogdan w nowych sytuacjach
PublicationW kolejnym odcinku serii z Alicją i Bogdanem najpierw ilustrujemy problem dominowania w grafach (kratowych): klasyczny i rzymski. Następnie ilustrujemy znany fakt, że zachłanność nie zawsze się opłaca. Pokażemy mianowicie, że algorytmy zachłanne nie gwarantują uzyskania rozwiązania optymalnego, nawet wówczas gdy problem da się rozwiązać w czasie wielomianowym.
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Quantum strategies for rendezvous and domination tasks on graphs with mobile agents
PublicationThis paper explores the application of quantum nonlocality, a renowned and unique phenomenon acknowledged as a valuable resource. Focusing on an alternative application, we demonstrate its quantum advantage for mobile agents engaged in specific distributed tasks without communication. The research addresses the significant challenge of rendezvous on graphs and introduces a distributed task for mobile agents grounded in the graph...
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Semi-definite programming and quantum information
PublicationThis paper presents a comprehensive exploration of semi-definite programming (SDP) techniques within the context of quantum information. It examines the mathematical foundations of convex optimization, duality, and SDP formulations, providing a solid theoretical framework for addressing optimization challenges in quantum systems. By leveraging these tools, researchers and practitioners can characterize classical and quantum correlations,...
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Teoria grafów wczoraj i dziś
PublicationW pracy naszkicowano kamienie milowe teorii grafów poczynając od pierwszego artykułu Eulera na temat mostów w Królewcu z połowy 18. wieku. Następnie opisano słynny problem 4 barw i jego wariacje. Pracę kończy charakterystyka najnowszych wyzwań teorii grafów.
Year 2023
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Complexity Issues on of Secondary Domination Number
PublicationIn this paper we study the computational complexity issues of the problem of secondary domination (known also as (1, 2)-domination) in several graph classes. We also study the computational complexity of the problem of determining whether the domination and secondary domination numbers are equal. In particular, we study the influence of triangles and vertices of degree 1 on these numbers. Also, an optimal algorithm for finding...
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Edge and Pair Queries-Random Graphs and Complexity
PublicationWe investigate two types of query games played on a graph, pair queries and edge queries. We concentrate on investigating the two associated graph parameters for binomial random graphs, and showing that determining any of the two parameters is NP-hard for bounded degree graphs.
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Edge coloring of graphs of signed class 1 and 2
PublicationRecently, Behr (2020) introduced a notion of the chromatic index of signed graphs and proved that for every signed graph (G, σ) it holds that ∆(G) ≤ χ′(G,σ) ≤ ∆(G) + 1, where ∆(G) is the maximum degree of G and χ′ denotes its chromatic index. In general, the chromatic index of (G, σ) depends on both the underlying graph G and the signature σ. In the paper we study graphs G for which χ′(G, σ) does not depend on σ. To this aim we...
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Entangled rendezvous: a possible application of Bell non-locality for mobile agents on networks
PublicationRendezvous is an old problem of assuring that two or more parties, initially separated, not knowing the position of each other, and not allowed to communicate, are striving to meet without pre-agreement on the meeting point. This problem has been extensively studied in classical computer science and has vivid importance to modern and future applications. Quantum non-locality, like Bell inequality violation, has shown that in many...
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Experimental certification of more than one bit of quantum randomness in the two inputs and two outputs scenario
PublicationOne of the striking properties of quantum mechanics is the occurrence of the Bell-type non-locality. They are a fundamental feature of the theory that allows two parties that share an entangled quantum system to observe correlations stronger than possible in classical physics. In addition to their theoretical significance, non-local correlations have practical applications, such as device-independent randomness generation, providing...
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Generalization of Phylogenetic Matching Metrics with Experimental Tests of Practical Advantages
PublicationThe ability to quantify a dissimilarity of different phylogenetic trees is required in various types of phylogenetic studies, for example, such metrics are used to assess the quality of phylogeny construction methods and to define optimization criteria in supertree building algorithms. In this article, starting from the already described concept of matching metrics, we define three new metrics for rooted phylogenetic trees. One...
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Grafo-mania, czyli rzecz o grafach i algorytmach. Gry chromatyczne na grafach.
PublicationW minieseju analizujemy grę 2-osobową, polegającą na tym, że Alicja i Bogdan współdziałają by pomalować mapę narysowaną na płaszczyźnie.
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Longitudinal drug synergy assessment using convolutional neural network image-decoding of glioblastoma single-spheroid cultures
PublicationAbstract Background In recent years, drug combinations have become increasingly popular to improve therapeutic outcomes in various diseases, including difficult to cure cancers such as the brain cancer glioblastoma. Assessing the interaction between drugs over time is critical for predicting drug combination effectiveness and minimizing the risk of therapy resistance. However, as viability readouts of drug combination experiments...
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Long-term mortality after transcatheter aortic valve implantation for aortic stenosis in immunosuppression-treated patients: a propensity-matched multicentre retrospective registry-based analysis
PublicationIntroduction Data regarding patients with a previous medical record of immunosuppression treatment who have undergone transcatheter aortic valve implantation (TAVI) are limited and extremely inconclusive. Available studies are mostly short term observations; thus there is a lack of evidence on efficacy and safety of TAVI in this specific group of patients. Aim To compare the in-hospital and long-term outcomes between patients...
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Platelet RNA Sequencing Data Through the Lens of Machine Learning
PublicationLiquid biopsies offer minimally invasive diagnosis and monitoring of cancer disease. This biosource is often analyzed using sequencing, which generates highly complex data that can be used using machine learning tools. Nevertheless, validating the clinical applications of such methods is challenging. It requires: (a) using data from many patients; (b) verifying potential bias concerning sample collection; and (c) adding interpretability...
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Potyczki algorytmiczne, czyli Alicja i Bogdan w nowych sytuacjach
PublicationPowracamy tutaj do zagadki sprzed 4 lat pod tym samym tytułem, którą uzupełniamy nowymi komentarzami i nowymi zagadkami na ten temat. Pozwala to nam zilustrować szerzej zasady działania algorytmu zachłannego.
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Potyczki algorytmiczne, czyli Alicja i Bogdan w nowych sytuacjach. 3. Alicja i Bogdan remontują mieszkanie.
PublicationPoniższe zagadki nawiązują z jednej strony do problemu kafelkowania płaszczyzny, który jest nierozstrzygalny, z drugiej do problemu rozkroju wstęgi, który jest NP-trudny. Jednakże przypadki szczególne, które tu rozważamy, nie są tak trudne i mogą być rozwiązane za pomocą algorytmów działających w czasie wielomianowym.
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Potyczki algorytmiczne, czyli Alicja i Bogdan w nowych sytuacjach. 4. Alicja i Bogdan w samochodzie.
PublicationZilustrowano problem przeszukiwania obiektów w nieznanych przestrzeniach na przykładzie jazdy samochodem.
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Potyczki algorytmiczne, czyli Alicja i Bogdan w nowych sytuacjach. 5. Alicja kupuje buty.
PublicationNiniejszy miniesej pokazuje, w jaki sposób można efektywnie przeszukiwać uporządkowane tablice 2-wymiarowe oraz, w jaki sposób można radzić sobie (niekiedy) z trudnymi problemami obliczeniowymi.
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Rekordowe liczby pierwsze
PublicationProblem liczb pierwszych ma długą historię sięgającą czasów starożytnych. W śród liczb całkowitych liczby pierwsze grają rolę analogiczną do pierwiastków w chemii.
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Screening of predicted synergistic multi-target therapies in glioblastoma identifies new treatment strategies
PublicationAbstract Background IDH-wildtype glioblastoma (GBM) is a highly malignant primary brain tumor with a median survival of 15 months after standard of care, which highlights the need for improved therapy. Personalized combination therapy has shown to be successful in many other tumor types and could be beneficial for GBM patients. Methods We performed the largest drug combination screen to date in GBM, using a high-throughput effort...
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Security of Cryptocurrencies: A View on the State-of-the-Art Research and Current Developments
Publication[Context] The goal of security is to protect digital assets, devices, and services from being disrupted, exploited or stolen by unauthorized users. It is also about having reliable information available at the right time. [Motivation] Since the inception in 2009 of the first cryptocurrency, few studies have been undertaken to analyze and review the state-of-the-art research and current developments with respect to the security...
Year 2022
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Application of Doubly Connected Dominating Sets to Safe Rectangular Smart Grids
PublicationSmart grids, together with the Internet of Things, are considered to be the future of the electric energy world. This is possible through a two-way communication between nodes of the grids and computer processing. It is necessary that the communication is easy and safe, and the distance between a point of demand and supply is short, to reduce the electricity loss. All these requirements should be met at the lowest possible cost....
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Efficacy of intralesional bleomycin in treatment resistant viral warts
PublicationIntroduction Optimal management of treatment-refractory viral warts caused by human papillomavirus is unknown. One of the treatment methods is intralesional bleomycin solution. Objective To determine risk factors for resistant viral warts (not responding to conventional treatments for ≥ 6 months), to determine the effectiveness and safety of intralesional bleomycin in a group of patients with viral warts resistant to conventional...
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Global defensive secure structures
PublicationLet S ⊂ V (G) for a given simple non-empty graph G. We define for any nonempty subset X of S the predicate SECG,S(X) = true iff |NG[X]∩S| ≥ |NG[X]\S|. Let H be a non-empty family of graphs such that for each vertex v ∈ V (G) there is a subgraph H of G containing v and isomorphic to a member of H. We introduce the concept of H-alliance extending the concept of global defensive secure structures. By an H-alliance in a graph G we...
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Grafo-ania, czyli rzecz o grafach i algorytmach. Drzewa Steinera
PublicationProblem: na płaszczyźnie leżą 3 punkty. Znajdź czwarty, taki że jego sumaryczna odległość od 3 pozostałych jest minimalna, Pokazujemy jak rozwiązać ten problem i jego uogólnienie.
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Grafo-mania, czyli rzecz o grafach i algorytmach. Liczby Ramseya
PublicationZdefiniowano liczby Ramseya i wskazano na trudności obliczeniowe ich wyznaczania już przy niewielkich wartościach takich liczb.
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Grafo-mania, czyli rzecz o grafach i algorytmach. Problem 8 hetmanów
PublicationW eseju spojrzano na problem 8 hetmanów na szachownicy z punktu widzenia teorii grafów
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Grafo-mania, czyli rzecz o grafach i algorytmach. Szybkie mnożenie macierzy
PublicationMiniesej zawiera komentarz na temat zastosowania sztucznej inteligencji do problemu mnożenia macierzy.
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Hybrid no-signaling-quantum correlations
PublicationFundamental investigations in non-locality have shown that while the no-signaling principle alone is not sufficient to single out the set of quantum non-local correlations, local quantum mechanics and no-signaling together exactly reproduce the set of quantum correlations in the two-party Bell scenario. Here, we introduce and study an intermediate hybrid no-signaling quantum set of non-local correlations that we term HNSQ in the...
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Infinite chromatic games
PublicationIn the paper we introduce a new variant of the graph coloring game and a new graph parameter being the result of the new game. We study their properties and get some lower and upper bounds, exact values for complete multipartite graphs and optimal, often polynomial-time strategies for both players provided that the game is played on a graph with an odd number of vertices. At the end we show that both games, the new and the classic...
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Non-Perfect Propagation of Information to a Noisy Environment with Self-Evolution
PublicationWe study the non-perfect propagation of information for evolving a low-dimensional environment that includes self-evolution as well as noisy initial states and analyse the interrelations between the degree of objectivization and environment parameters. In particular, we consider an analytical model of three interacting qubits and derive its objectivity parameters. The numerical analysis shows that the quality of the spectrum broadcast...
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On zero-error codes produced by greedy algorithms
PublicationWe present two greedy algorithms that determine zero-error codes and lower bounds on the zero-error capacity. These algorithms have many advantages, e.g., they do not store a whole product graph in a computer memory and they use the so-called distributions in all dimensions to get better approximations of the zero-error capacity. We also show an additional application of our algorithms.
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Paired domination versus domination and packing number in graphs
PublicationGiven a graph G = (V(G), E(G)), the size of a minimum dominating set, minimum paired dominating set, and a minimum total dominating set of a graph G are denoted by γ (G), γpr(G), and γt(G), respectively. For a positive integer k, a k-packing in G is a set S ⊆ V(G) such that for every pair of distinct vertices u and v in S, the distance between u and v is at least k + 1. The k-packing number is the order of a largest kpacking and...
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Polynomial Algorithm for Minimal (1,2)-Dominating Set in Networks
PublicationDominating sets find application in a variety of networks. A subset of nodes D is a (1,2)-dominating set in a graph G=(V,E) if every node not in D is adjacent to a node in D and is also at most a distance of 2 to another node from D. In networks, (1,2)-dominating sets have a higher fault tolerance and provide a higher reliability of services in case of failure. However, finding such the smallest set is NP-hard. In this paper, we...
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Potyczki algorytmiczne, czyli Alicja i Bogdan w nowych sytuacjach. Alicja i Bogdan w naleśnikarni
PublicationNiniejszym esejem inaugurujemy , po kilkuletniej przerwie, nową serię zagadek algorytmicznych.Pierwszy odcinek nosi nazwę Alicja i Bogdan w naleśnikarni.
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Quantum security and theory of decoherence
PublicationWe sketch a relation between two crucial, yet independent, fields in quantum information research, viz. quantum decoherence and quantum cryptography. We investigate here how the standard cryptographic assumption of shielded laboratory, stating that data generated by a secure quantum device remain private unless explicitly published, is disturbed by the einselection mechanism of quantum Darwinism explaining the measurement process...
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Scheduling on Uniform and Unrelated Machines with Bipartite Incompatibility Graphs
PublicationThe problem of scheduling jobs on parallel machines under an incompatibility relation is considered in this paper. In this model, a binary relation between jobs is given and no two jobs that are in the relation can be scheduled on the same machine. We consider job scheduling under the incompatibility relation modeled by a bipartite graph, under the makespan optimality criterion, on uniform and unrelated machines. Unrelated machines...
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Scheduling with Complete Multipartite Incompatibility Graph on Parallel Machines: Complexity and Algorithms
PublicationIn this paper, the problem of scheduling on parallel machines with a presence of incompatibilities between jobs is considered. The incompatibility relation can be modeled as a complete multipartite graph in which each edge denotes a pair of jobs that cannot be scheduled on the same machine. The paper provides several results concerning schedules, optimal or approximate with respect to the two most popular criteria of optimality:...
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Significance of Dermoscopy in Association with Clinical Features in Differentiation of Basal Cell Carcinoma and Benign Trichoblastic Tumours
PublicationBackground: Although basal cell carcinoma (BCC) can, in the majority of cases, be diagnosed based on clinical and dermoscopic assessment, a potential overlap with benign adnexal skin tumours seems to exist, including trichoblastic tumours (TT). Methods: Retrospective analysis of clinical and dermoscopic features of benign TT and BCC cases was performed to develop a diagnostic algorithm with a potential utility in clinical practice....
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Weighted 2-sections and hypergraph reconstruction
PublicationIn the paper we introduce the notion of weighted 2-sections of hypergraphs with integer weights and study the following hypergraph reconstruction problems: (1) Given a weighted graph , is there a hypergraph H such that is its weighted 2-section? (2) Given a weighted 2-section , find a hypergraph H such that is its weighted 2-section. We show that (1) is NP-hard even if G is a complete graph or integer weights w does not exceed...
Year 2021
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Block graphs with large paired domination multisubdivision number
PublicationThe paired domination multisubdivision number of a nonempty graph G, denoted by msdpr(G), is the smallest positive integer k such that there exists an edge which must be subdivided k times to increase the paired domination number of G. It is known that msdpr(G) ≤ 4 for all graphs G. We characterize block graphs with msdpr(G) = 4.
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Bortezomib induces methylation changes in neuroblastoma cells that appear to play a significant role in resistance development to this compound
PublicationThe anticancer activity of bortezomib (BTZ) has been increasingly studied in a number of indications and promising results for the use of this treatment have been shown in neuroblastoma. As BTZ treatment is usually administered in cycles, the development of resistance and side effects in patients undergoing therapy with BTZ remains a major challenge for the clinical usage of this compound. Common resistance development also means...
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Bounds on isolated scattering number
PublicationThe isolated scattering number is a parameter that measures the vulnerability of networks. This measure is bounded by formulas de- pending on the independence number. We present new bounds on the isolated scattering number that can be calculated in polynomial time.
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Bounds on isolated scattering number
PublicationThe isolated scattering number is a parameter that measures the vulnerability of networks. This measure is bounded by formulas de- pending on the independence number. We present new bounds on the isolated scattering number that can be calculated in polynomial time.
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Closer Look at the Uncertainty Estimation in Semantic Segmentation under Distributional Shift
PublicationWhile recent computer vision algorithms achieve impressive performance on many benchmarks, they lack robustness - presented with an image from a different distribution, (e.g. weather or lighting conditions not considered during training), they may produce an erroneous prediction. Therefore, it is desired that such a model will be able to reliably predict its confidence measure. In this work, uncertainty estimation for the task...
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Diagnostic Accuracy of Liquid Biopsy in Endometrial Cancer
PublicationBackground: Liquid biopsy is a minimally invasive collection of a patient body fluid sample. In oncology, they offer several advantages compared to traditional tissue biopsies. However, the potential of this method in endometrial cancer (EC) remains poorly explored. We studied the utility of tumor educated platelets (TEPs) and circulating tumor DNA (ctDNA) for preoperative EC diagnosis, including histology determination. Methods:...
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Gossiping by energy-constrained mobile agents in tree networks
PublicationEvery node of an edge-weighted tree network contains a data packet. At some nodes are placed mobile agents, each one possessing an amount of energy (not necessarily the same for all agents). While walking along the network, the agents spend the energy proportionally to the distance traveled and collect copies of the data packets present at the visited network nodes. An agent visiting a node deposits there copies of all currently...