Quantum request-answer game with buffer model for online algorithms. Application for The Most Frequent Keyword Problem

We consider online algorithms as a request-answer game. An adversary that generates input requests, and an online algorithm answers. We consider a generalized version of the game that has a buffer of limited size. The adversary loads data to the buffer, and the algorithm has random access to elements of the buffer. We consider quantum and classical (deterministic or randomized) algorithms for the model. In the paper, we provide a specific problem (The Most Frequent Keyword Problem) and a quantum algorithm that works better than any classical (deterministic or randomized) algorithm in terms of competitive ratio. At the same time, for the problem, classical online algorithms in the standard model are equivalent to the classical algorithms in the request-answer game with buffer model.We consider online algorithms as a request-answer game. An adversary that generates input requests, and an online algorithm answers. We consider a generalized version of the game that has a buffer of limited size. The adversary loads data to the buffer, and the algorithm has random access to elements of the buffer. We consider quantum and classical (deterministic or randomized) algorithms for the model. In the paper, we provide a specific problem (The Most Frequent Keyword Problem) and a quantum algorithm that works better than any classical (deterministic or randomized) algorithm in terms of competitive ratio. At the same time, for the problem, classical online algorithms in the standard model are equivalent to the classical algorithms in the request-answer game with buffer model.

arXiv:2012.12321Dec 22, 20201 citation

Quantum Online Algorithms for a Model of the Request-Answer Game with a Buffer

Kamil Ravilevich Khadiev, Dianhuan Lin

In this paper, we considered online algorithms as a request-answer game between two players: an adversary that generates input requests and an online algorithm that answers them. A generalized version of the game that has a buffer of limited size was studied. The adversary loads data to the buffer, while the algorithm has random access to elements of the buffer. For the model, quantum and classical (deterministic or randomized) algorithms were a focus of attention. A specific problem and a quantum algorithm that works better than any classical (deterministic or randomized) algorithm, in terms of competitive ratio, were provided. At the same time, for the problem, classical online algorithms in the standard model are equivalent to the classical algorithms in the request-answer game with a buffer model.In this paper, we considered online algorithms as a request-answer game between two players: an adversary that generates input requests and an online algorithm that answers them. A generalized version of the game that has a buffer of limited size was studied. The adversary loads data to the buffer, while the algorithm has random access to elements of the buffer. For the model, quantum and classical (deterministic or randomized) algorithms were a focus of attention. A specific problem and a quantum algorithm that works better than any classical (deterministic or randomized) algorithm, in terms of competitive ratio, were provided. At the same time, for the problem, classical online algorithms in the standard model are equivalent to the classical algorithms in the request-answer game with a buffer model.

Učenye zapiski Kazanskogo gosudarstvennogo universiteta. Seriâ Fiziko-matematičeskie nauki/Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie naukiJan 1, 20207 citations

Quantum Online Streaming Algorithms with Constant Number of Advice Bits.

Kamil Ravilevich Khadiev, Mansur Ziatdinov, Ilnaz Mannapov +2 more

Online algorithms are known model that is investigated with respect to a competitive ratio typically. In this paper, we investigate streaming algorithms as a model for online algorithms. We focus on quantum and classical online algorithms with advice. Special problem $P_k$ was considered. This problem is obtained using Black Hats Method. There is an optimal quantum online algorithm with single advice bit and single qubit of memory for the problem. At the same time, there is no optimal deterministic or randomized online algorithm with sublogarithmic memory for the same problem even the algorithm gets $o(\log n)$ advice bits. Additionally, we show that quantum online algorithm with a constant number of qubits can be better than deterministic online algorithm even if deterministic one has a constant number of advice bits and unlimited computational power.Online algorithms are known model that is investigated with respect to a competitive ratio typically. In this paper, we investigate streaming algorithms as a model for online algorithms. We focus on quantum and classical online algorithms with advice. Special problem $P_k$ was considered. This problem is obtained using Black Hats Method. There is an optimal quantum online algorithm with single advice bit and single qubit of memory for the problem. At the same time, there is no optimal deterministic or randomized online algorithm with sublogarithmic memory for the same problem even the algorithm gets $o(\log n)$ advice bits. Additionally, we show that quantum online algorithm with a constant number of qubits can be better than deterministic online algorithm even if deterministic one has a constant number of advice bits and unlimited computational power.

Feb 13, 20185 citations

Quantum versus Classical Online Streaming Algorithms with Advice

Kamil Ravilevich Khadiev, Aliya Khadieva, Mansur Ziatdinov +4 more

We consider online algorithms with respect to the competitive ratio. Here, we investigate quantum and classical one-way automata with non-constant size of memory (streaming algorithms) as a model for online algorithms. We construct problems that can be solved by quantum online streaming algorithms better than by classical ones in a case of logarithmic or sublogarithmic size of memory, even if classical online algorithms get advice bits. Furthermore, we show that a quantum online algorithm with a constant number of qubits can be better than any deterministic online algorithm with a constant number of advice bits and unlimited computational power.We consider online algorithms with respect to the competitive ratio. Here, we investigate quantum and classical one-way automata with non-constant size of memory (streaming algorithms) as a model for online algorithms. We construct problems that can be solved by quantum online streaming algorithms better than by classical ones in a case of logarithmic or sublogarithmic size of memory, even if classical online algorithms get advice bits. Furthermore, we show that a quantum online algorithm with a constant number of qubits can be better than any deterministic online algorithm with a constant number of advice bits and unlimited computational power.

arXiv:1802.05134Feb 13, 20180 citations

Quantum Online Algorithms with Respect to Space Complexity

Kamil Ravilevich Khadiev, Aliya Khadieva, Ilnaz Mannapov

Online algorithm is a well-known computational model. We introduce quantum online algorithms and investigate them with respect to a competitive ratio in two points of view: space complexity and advice complexity. We start with exploring a model with restricted memory and show that quantum online algorithms can be better than classical ones (deterministic or randomized) for sublogarithmic space (memory), and they can be better than deterministic online algorithms without restriction for memory. Additionally, we consider polylogarithmic space case and show that in this case, quantum online algorithms can be better than deterministic ones as well.Online algorithm is a well-known computational model. We introduce quantum online algorithms and investigate them with respect to a competitive ratio in two points of view: space complexity and advice complexity. We start with exploring a model with restricted memory and show that quantum online algorithms can be better than classical ones (deterministic or randomized) for sublogarithmic space (memory), and they can be better than deterministic online algorithms without restriction for memory. Additionally, we consider polylogarithmic space case and show that in this case, quantum online algorithms can be better than deterministic ones as well.

arXiv:1709.08409Sep 25, 20173 citations

Quantum Online Algorithms with Respect to Space and Advice Complexity

Kamil Ravilevich Khadiev, Aliya Khadieva, Ilnaz Mannapov

Online computation is a well-known area of computer science. We introduce quantum online algorithms and investigate them with respect to a competitive ratio in two points of view: space complexity and advice complexity. We start with exploring a model with restricted memory and show that quantum online algorithms can be better than classical ones (deterministic or randomized) for sublogarithmic space (memory), and they can be better than deterministic online algorithms without restriction for memory. Additionally, we consider the polylogarithmic space case and show that in this case, quantum online algorithms can be better than deterministic ones as well. Another point of view to the online algorithms model is advice complexity. So, we introduce quantum online algorithms with a quantum channel with an adviser. Firstly, we show that quantum algorithms have at least the same computational power as classical ones have. We give some examples of quantum online algorithms with advice. Secondly, we show that if we allow to use shared entangled qubits (EPR-pairs), then a quantum online algorithm can use half as many advise qubits compared to a classical one. We apply this approach to the well-known Paging Problem.Online computation is a well-known area of computer science. We introduce quantum online algorithms and investigate them with respect to a competitive ratio in two points of view: space complexity and advice complexity. We start with exploring a model with restricted memory and show that quantum online algorithms can be better than classical ones (deterministic or randomized) for sublogarithmic space (memory), and they can be better than deterministic online algorithms without restriction for memory. Additionally, we consider the polylogarithmic space case and show that in this case, quantum online algorithms can be better than deterministic ones as well. Another point of view to the online algorithms model is advice complexity. So, we introduce quantum online algorithms with a quantum channel with an adviser. Firstly, we show that quantum algorithms have at least the same computational power as classical ones have. We give some examples of quantum online algorithms with advice. Secondly, we show that if we allow to use shared entangled qubits (EPR-pairs), then a quantum online algorithm can use half as many advise qubits compared to a classical one. We apply this approach to the well-known Paging Problem.

Lobachevskii Journal of MathematicsNov 1, 201832 citations

P_k

was considered. This problem is obtained using Black Hats Method. There is an optimal quantum online algorithm with single advice bit and single qubit of memory for the problem. At the same time, there is no optimal deterministic or randomized online algorithm with sublogarithmic memory for the same problem even the algorithm gets

o(\log n)

advice bits. Additionally, we show that quantum online algorithm with a constant number of qubits can be better than deterministic online algorithm even if deterministic one has a constant number of advice bits and unlimited computational power.