Error-Tolerant Exact Query Learning of Finite Set Partitions with Same-Cluster Oracle

This paper initiates the study of active learning for exact recovery of partitions exclusively through access to a same-cluster oracle in the presence of bounded adversarial error. We first highlight a novel connection between learning partitions and correlation clustering. Then we use this connection to build a R\'enyi-Ulam style analytical framework for this problem, and prove upper and lower bounds on its worst-case query complexity. Further, we bound the expected performance of a relevant randomized algorithm. Finally, we study the relationship between adaptivity and query complexity for this problem and related variants.Comment: 28 pages, 2 figure

Pengembangan Algoritma Pencarian Non Interaktif untuk Penyelesaian Permasalahan Ulam dengan Kebohongan Jamak

Pada permasalahan permainan klasik pencarian Ulam dan Rényi, penanya harus mengajukan beberapa pertanyaan iya dan tidak untuk mencari sebuah nilai dalam range pencarian yang sudah disepakati, namun penjawab diperbolehkan berbohong. Sudah ada solusi dari beberapa variasi pada permasalahan pencarian Ulam dan Rényi, yaitu pada jenis query antara rentang atau subset dan jumlah maksimal bohong antara satu, dua, tiga, dan seterusnya. Namun belum ada solusi yang sempurna untuk query yang non interaktif yaitu penjawab hanya boleh menjawab query penanya setelah penanya selesai menanyakan semua querynya. Belum ada penelitian yang menyelesaikan permasalahan ini. Pada paper ini akan dijelaskan solusi sempurna untuk permainan Ulam dan Rényi non interaktif dengan maksimal kebohongan jamak menggunakan kode biner dengan jarak Hamming. Hasil algoritma pada paper ini menunjukkan jumlah query yang jauh lebih sedikit dari algoritma umum repetisi biner dan hasil terbaik pada pengujian online ternama. ============================ On the classic Ulam and Rényi searching problem, the questioner has to ask some yes-no questions to find an unknown value within the agreed search space, but the answerer is allowed to lie. There are already solutions of some variations in the Ulam and Rényi searching problem, i.e. on the type of query between range or subset and the maximum number of lies between one, two, three, and so on. But there is no perfect solution for non-interactive queries which the answerer can only answer the questioner's query after the questioner has finished querying all the queries. No research has resolved this problem yet. In this paper we will describe the perfect solution for non-interactive Ulam and Rényi searching problem with many lies using binary code with Hamming distance. The algorithm results in this paper shows a much smaller number of queries than the common binary repetition algorithm and the best results on a reputable online judge

Binary search in graphs revisited

In the classical binary search in a path the aim is to detect an unknown target by asking as few queries as possible, where each query reveals the direction to the target. This binary search algorithm has been recently extended by Emamjomeh-Zadeh et al. (in: Proceedings of the 48th annual ACM SIGACT symposium on theory of computing, STOC 2016, Cambridge, pp. 519–532, 2016) to the problem of detecting a target in an arbitrary graph. Similarly to the classical case in the path, the algorithm of Emamjomeh-Zadeh et al. maintains a candidates’ set for the target, while each query asks an appropriately chosen vertex—the “median”—which minimises a potential Φ among the vertices of the candidates’ set. In this paper we address three open questions posed by Emamjomeh-Zadeh et al., namely (a) detecting a target when the query response is a direction to an approximately shortest path to the target, (b) detecting a target when querying a vertex that is an approximate median of the current candidates’ set (instead of an exact one), and (c) detecting multiple targets, for which to the best of our knowledge no progress has been made so far. We resolve questions (a) and (b) by providing appropriate upper and lower bounds, as well as a new potential Γ that guarantees efficient target detection even by querying an approximate median each time. With respect to (c), we initiate a systematic study for detecting two targets in graphs and we identify sufficient conditions on the queries that allow for strong (linear) lower bounds and strong (polylogarithmic) upper bounds for the number of queries. All of our positive results can be derived using our new potential Γ that allows querying approximate medians

The role of structures in collective processes

In this thesis we study the dynamics of social systems and molecular monolayers employing tools of statistical physics. In both cases the topological structure underlying the interactions turns out to be the key element in the emergence of collective macroscopic phenomena from the synergy of the individual interactions

LIPIcs, Volume 251, ITCS 2023, Complete Volume

LIPIcs, Volume 251, ITCS 2023, Complete Volum

Schelling's Bounded Neighbourhood Model: A systematic investigation

This thesis explores the role of modelling and computational simulation, in relation to social systems, with specific focus on Schelling's Bounded Neighbourhood Model. It discusses the role of computational modelling and some techniques that can be used in the Social sciences. Simulation of social interaction consistently creates debate in the Social sciences. However, most models are dismissed as either too simplistic or unrealistic. In an attempt to counter these criticisms, more complex models have been developed. However, by increasing the complexity of the model, the underlying dynamics can be lost. Schelling's models of segregation are a classic example, with much of the work building on his simple segregation model. The complexity of the models being developed are such that, real world implications are being inferred from the results. The Complex Systems Modelling and Simulation (CoSMoS) process has a proven track record in developing simulations of complex models. In a novel application, the CoSMoS process is applied to Schelling's Bounded Neighbourhood Model. The process formalises Schelling's Bounded Neighbourhood Model and develops a simulation. The simulation is validated against the results from Schelling's model and then used to question the model. The questioning of the model is an attempt to examine the underlying dynamics of the segregation model. In this respect, two measures, static and dynamic, are used in the analysis of the results. Initally, the effect of ordered movement was tested by changing the movement, from ordered to random. A second experiment examined agents' perfect knowledge of the system. By introducing a sample, the agents' knowledge of the system is reduced. The third experiment introduced a friction parameter, to examine the effect of ease of movement into and out of the neighbourhood. In the final experiment, Schelling's model is recast as a network model. Although the recasting of the model is slightly unorthodox, it opens the model up to network analysis. This analysis allows the easy definition of a `social network' that is overlaid on Schelling's `neighbourhood network'. Two different networks are applied, Random and Small World. The results of the experiments showed, that Schelling's model is remarkably robust. Whilst the adjustments to the model all contributed to changes in the output, the only significant difference occurred when the social network was added