Year: 2024
Type: article
Abstract: It is natural to generalize the online $$k$$ k -Server problem by allowing each request to specify not only a point p, but also a subset S of servers that may serve it. To date, only a few special cases of this problem have been studied. The objective of the work presented in this paper has been to more systematically explore this generalization in the case of uniform and star metrics. For uniform metrics, the problem is equivalent to a generalization of Paging in which each request specifies not only a page p, but also a subset S of cache slots, and is satisfied by having a copy of p in some slot in S. We call this problem Slot-Heterogenous Paging. In realistic settings only certain subsets of cache slots or servers would appear in requests. Therefore we parameterize the problem by specifying a family $${\mathcal {S}}\subseteq 2^{[k]}$$ S ⊆ 2 [ k ] of requestable slot sets, and we establish bounds on the competitive ratio as a function of the cache size k and family $${\mathcal {S}}$$ S : If all request sets are allowed ( $${\mathcal {S}}=2^{[k]}\setminus \{\emptyset \}$$ S = 2 [ k ] \ { ∅ } ), the optimal deterministic and randomized competitive ratios are exponentially worse than for standard Paging ( $${\mathcal {S}}=\{[k]\}$$ S = { [ k ] } ). As a function of $$|{\mathcal {S}}|$$ | S | and k, the optimal deterministic ratio is polynomial: at most $$O(k^2|{\mathcal {S}}|)$$ O ( k 2 | S | ) and at least $$\Omega (\sqrt{|{\mathcal {S}}|})$$ Ω ( | S | ) . For any laminar family $${\mathcal {S}}$$ S of height h, the optimal ratios are O(hk) (deterministic) and $$O(h^2\log k)$$ O ( h 2 log k ) (randomized). The special case of laminar $${\mathcal {S}}$$ S that we call All-or-One Paging extends standard Paging by allowing each request to specify a specific slot to put the requested page in. The optimal deterministic ratio for weighted All-or-One Paging is $$\Theta (k)$$ Θ ( k ) . Offline All-or-One Paging is
Source: Algorithmica
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
Awards: G2318107623, AF: Small: Embedding Distributed Computations and Flows in Networks, AF: Small: Allocation Algorithms in Online Systems, AF:Small: Distributed Protocols for Information Dissemination in Ad-Hoc Radio Networks, G3231041619, G3664224518, Collaborative Research: AF: Medium: Algorithms Meet Machine Learning: Mitigating Uncertainty in Optimization, AitF: FULL: Collaborative Research: Optimizing Networked Systems with Limited Information, CAREER: New Directions in Graph Algorithms, III: Small: Increase the Throughput of Non-Relational Databases through Theoretical Modeling and Optimization, AitF: FULL: Collaborative Research: Optimizing Networked Systems with Limited Information, D-ISN: TRACK 2: Collaborative Research: Financial Network Disruptions in Illicit and Counterfeit Medicines (FIND-M), AitF: EXPL: Algorithmic Fluid Concentration Management for Programmable Microfluidics, G7501076386, G7920133051, G999382238
OpenAlex ID: W4403490672