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Documents authored by Wasim, Omer

Document
DOI: 10.4230/LIPIcs.ITCS.2025.81
Online Balanced Allocation of Dynamic Components

Authors: Rajmohan Rajaraman and Omer Wasim

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

Abstract
We introduce Online Balanced Allocation of Dynamic Components (OBADC), a problem motivated by the practical challenge of dynamic resource allocation for large-scale distributed applications. In OBADC, we need to allocate a dynamic set of at most k𝓁 vertices (representing processes) in 𝓁 > 0 clusters. We consider an over-provisioned setup in which each cluster can hold at most k(1+ε) vertices, for an arbitrary constant ε > 0. The communication requirements among the vertices are modeled by the notion of a dynamically changing component, which is a subset of vertices that need to be co-located in the same cluster. At each time t, a request r_t of one of the following types arrives: 1) insertion of a vertex v forming a singleton component v at unit cost. 2) merge of (u,v) requiring that the components containing u and v be merged and co-located thereafter. 3) deletion of an existing vertex v at zero cost. Before serving any request, an algorithm can migrate vertices from one cluster to another, at a unit migration cost per vertex. We seek an online algorithm to minimize the total migration cost incurred for an arbitrary request sequence σ = (r_t)_{t > 0}, while simultaneously minimizing the number of clusters utilized. We analyze competitiveness with respect to an optimal clairvoyant offline algorithm with identical (over-provisioned) capacity constraints. We give an O(log k)-competitive algorithm for OBADC, and a matching lower-bound. The number of clusters utilized by our algorithm is always within a (2+ε) factor of the minimum. Furthermore, in a resource augmented setting where the optimal offline algorithm is constrained to capacity k per cluster, our algorithm obtains O(log k) competitiveness and utilizes a number of clusters within (1+ε) factor of the minimum. We also consider OBADC in the context of machine-learned predictions, where for each newly inserted vertex v at time t: i) with probability η > 0, the set of vertices (that exist at time t) in the component of v is revealed and, ii) with probability 1-η, no information is revealed. For OBADC with predictions, we give a O(1)-consistent and O(min(log 1/(η), log k))-robust algorithm.
Cite as

Rajmohan Rajaraman and Omer Wasim. Online Balanced Allocation of Dynamic Components. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 81:1-81:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{rajaraman_et_al:LIPIcs.ITCS.2025.81,
  author =	{Rajaraman, Rajmohan and Wasim, Omer},
  title =	{{Online Balanced Allocation of Dynamic Components}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{81:1--81:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.81},
  URN =		{urn:nbn:de:0030-drops-227090},
  doi =		{10.4230/LIPIcs.ITCS.2025.81},
  annote =	{Keywords: online algorithms, competitive ratio, algorithms with predictions}
}
Document
DOI: 10.4230/LIPIcs.ESA.2024.95
Competitive Capacitated Online Recoloring

Authors: Rajmohan Rajaraman and Omer Wasim

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
In this paper, we revisit the online recoloring problem introduced recently by Azar, Machluf, Patt-Shamir and Touitou [Azar et al., 2022] to investigate algorithmic challenges that arise while scheduling virtual machines or processes in distributed systems and cloud services. In online recoloring, there is a fixed set V of n vertices and an initial coloring c₀: V → [k] for some k ∈ ℤ^{> 0}. Under an online sequence σ of requests where each request is an edge (u_t,v_t), a proper vertex coloring c of the graph G_t induced by requests until time t needs to be maintained for all t; i.e., for any (u,v) ∈ G_t, c(u)≠ c(v). In the distributed systems application, a vertex corresponds to a VM, an edge corresponds to the requirement that the two endpoint VMs be on different clusters, and a coloring is an allocation of VMs to clusters. The objective is to minimize the total weight of vertices recolored for the sequence σ. In [Azar et al., 2022], the authors give competitive algorithms for two polynomially tractable cases - 2-coloring for bipartite G_t and (Δ+1)-coloring for Δ-degree G_t - and lower bounds for the fully dynamic case where G_t can be arbitrary. We obtain the first competitive algorithms for capacitated online recoloring and fully dynamic recoloring, in which there is a bound on the number or weight of vertices in each color. Our first set of results is for 2-recoloring using algorithms that are (1+ε)-resource augmented where ε ∈ (0,1) is an arbitrarily small constant. Our main result is an O(log n)-competitive deterministic algorithm for weighted bipartite graphs, which is asymptotically optimal in light of an Ω(log n) lower bound that holds for an unbounded amount of augmentation. We also present an O(nlog n)-competitive deterministic algorithm for fully dynamic recoloring, which is optimal within an O(log n) factor in light of a Ω(n) lower bound that holds for an unbounded amount of augmentation. Our second set of results is for Δ-recoloring in an (1+ε)-overprovisioned setting where the maximum degree of G_t is bounded by (1-ε)Δ for all t, and each color assigned to at most (1+ε)n/(Δ) vertices, for an arbitrary ε > 0. Our main result is an O(1)-competitive randomized algorithm for Δ = O(√{n/log n}). We also present an O(Δ)-competitive deterministic algorithm for Δ ≤ ε n/2. Both results are asymptotically optimal.
Cite as

Rajmohan Rajaraman and Omer Wasim. Competitive Capacitated Online Recoloring. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 95:1-95:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{rajaraman_et_al:LIPIcs.ESA.2024.95,
  author =	{Rajaraman, Rajmohan and Wasim, Omer},
  title =	{{Competitive Capacitated Online Recoloring}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{95:1--95:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.95},
  URN =		{urn:nbn:de:0030-drops-211666},
  doi =		{10.4230/LIPIcs.ESA.2024.95},
  annote =	{Keywords: online algorithms, competitive ratio, recoloring, resource augmentation}
}
Document
DOI: 10.4230/LIPIcs.ESA.2022.83
Improved Bounds for Online Balanced Graph Re-Partitioning

Authors: Rajmohan Rajaraman and Omer Wasim

Published in: LIPIcs, Volume 244, 30th Annual European Symposium on Algorithms (ESA 2022)

Abstract
We study the online balanced graph re-partitioning problem (OBGR) which was introduced by Avin, Bienkowski, Loukas, Pacut, and Schmid [Avin et al., 2020] and has recently received significant attention [Pacut et al., 2021; Henzinger et al., 2021; Henzinger et al., 2019; Tobias Forner et al., 2021; Bienkowski et al., 2021] owing to potential applications in large-scale, data-intensive distributed computing. In OBGR, we have a set of 𝓁 clusters, each with k vertices (representing processes or virtual machines), and an online sequence of communication requests, each represented by a pair of vertices. Any request (u,v) incurs unit communication cost if u and v are located in different clusters (and zero otherwise). Any vertex can be migrated from one cluster to another at a migration cost of α ≥ 1. We consider the objective of minimizing the total communication and migration cost in the competitive analysis framework. The only known algorithms (which run in exponential time) include an O(k²𝓁²) competitive [Avin et al., 2020] and an O(k𝓁 2^O(k)) competitive algorithm [Bienkowski et al., 2021]. A lower bound of Ω(k𝓁) is known [Pacut et al., 2021]. In an effort to bridge the gap, recent results have considered beyond worst case analyses including resource augmentation (with augmented cluster capacity [Avin et al., 2020; Henzinger et al., 2019; Henzinger et al., 2021]) and restricted request sequences (the learning model [Henzinger et al., 2019; Henzinger et al., 2021; Pacut et al., 2021]). In this paper, we give deterministic, polynomial-time algorithms for OBGR, which mildly exploit resource augmentation (i.e. augmented cluster capacity of (1+ε) k for arbitrary ε > 0). We improve beyond O(k²𝓁²)-competitiveness (for general 𝓁, k) by first giving a simple algorithm with competitive ratio O(k𝓁²log k). Our main result is an algorithm with a significantly improved competitive ratio of O(k𝓁 log k). At a high level, we achieve this by employing i) an ILP framework to guide the allocation of large components, ii) a simple "any fit" style assignment of small components and iii) a charging argument which allows us to bound the cost of migrations. Like previous work on OBGR, our algorithm and analysis are phase-based, where each phase solves an independent instance of the learning model. Finally, we give an Ω(α k𝓁 log k) lower bound on the total cost incurred by any algorithm for OBGR under the learning model, which quantifies the limitation of a phase-based approach.
Cite as

Rajmohan Rajaraman and Omer Wasim. Improved Bounds for Online Balanced Graph Re-Partitioning. In 30th Annual European Symposium on Algorithms (ESA 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 244, pp. 83:1-83:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{rajaraman_et_al:LIPIcs.ESA.2022.83,
  author =	{Rajaraman, Rajmohan and Wasim, Omer},
  title =	{{Improved Bounds for Online Balanced Graph Re-Partitioning}},
  booktitle =	{30th Annual European Symposium on Algorithms (ESA 2022)},
  pages =	{83:1--83:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-247-1},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{244},
  editor =	{Chechik, Shiri and Navarro, Gonzalo and Rotenberg, Eva and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2022.83},
  URN =		{urn:nbn:de:0030-drops-170210},
  doi =		{10.4230/LIPIcs.ESA.2022.83},
  annote =	{Keywords: online algorithms, graph partitioning, competitive analysis}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2020.33
Fully Dynamic Sequential and Distributed Algorithms for MAX-CUT

Authors: Omer Wasim and Valerie King

Published in: LIPIcs, Volume 182, 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)

Abstract
This paper initiates the study of the MAX-CUT problem in fully dynamic graphs. Given a graph G = (V,E), we present deterministic fully dynamic distributed and sequential algorithms to maintain a cut on G which always contains at least |E|/2 edges in sublinear update time under edge insertions and deletions to G. Our results include the following deterministic algorithms: i) an O(Δ) worst-case update time sequential algorithm, where Δ denotes the maximum degree of G, ii) the first fully dynamic distributed algorithm taking O(1) rounds and O(Δ) total bits of communication per update in the Massively Parallel Computation (MPC) model with n machines and O(n) words of memory per machine. The aforementioned algorithms require at most one adjustment, that is, a move of one vertex from one side of the cut to the other. We also give the following fully dynamic sequential algorithms: i) a deterministic O(m^{1/2}) amortized update time algorithm where m denotes the maximum number of edges in G during any sequence of updates and, ii) a randomized algorithm which takes Õ(n^{2/3}) worst-case update time when edge updates come from an oblivious adversary.
Cite as

Omer Wasim and Valerie King. Fully Dynamic Sequential and Distributed Algorithms for MAX-CUT. In 40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 182, pp. 33:1-33:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{wasim_et_al:LIPIcs.FSTTCS.2020.33,
  author =	{Wasim, Omer and King, Valerie},
  title =	{{Fully Dynamic Sequential and Distributed Algorithms for MAX-CUT}},
  booktitle =	{40th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2020)},
  pages =	{33:1--33:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-174-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{182},
  editor =	{Saxena, Nitin and Simon, Sunil},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2020.33},
  URN =		{urn:nbn:de:0030-drops-132746},
  doi =		{10.4230/LIPIcs.FSTTCS.2020.33},
  annote =	{Keywords: data structures, dynamic graph algorithms, approximate maximum cut, distributed computing, parallel computing}
}
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