arXiv subjects

Alireza Kaviani

Publications and source records attributed to Alireza Kaviani.

6 recordsLinked to original sources

arXiv2026

Breaking the Exponential Barrier: The First Polynomial-Time Algorithm for the Gy\H{o}ri-Lov\'asz Theorem

We give the first polynomial-time algorithm, after half a century, for the celebrated Gy\H{o}ri-Lov\'asz theorem, which resolved a conjecture of Frank (1975). The theorem, one of the simplest existential theorems to explain, states that every $k$-connected graph can be partitioned into $k$ disjoint connected subgraphs of arbitrary prescribed positive sizes. This is a fundamental structural result with broad applications, such as flexible allocation of connected subnetworks of prescribed sizes in sufficiently connected cloud infrastructures. While Lov\'asz (1977) gave a highly non-constructive proof for a stronger directed version using algebraic topology, Gy\H{o}ri's original constructive proof (1976) requires exponential time. Despite more than 50 years of effort, no polynomial-time algorithm was known even for $k>4$. Determining the computational complexity of the Gy\H{o}ri-Lov\'asz theorem---whether it admits even a sub-exponential-time algorithm or is computationally hard (in particular, PLS-complete or PPAD)---has remained one of the central open problems in algorithmic graph theory. In this paper, we finally resolve this long-standing problem by a fundamentally new proof of the existential theorem via introducing the novel concept of \emph{flow-essential assignment}, which genuinely marries matching and cut structures and yields the first polynomial-time constructive algorithm for the Gy\H{o}ri-Lov\'asz theorem. In fact, we obtain a polynomial-time algorithm for Lov\'asz's stronger directed version, whose proof was non-constructive even for DAGs; for DAGs, we further obtain a near-linear-time algorithm. We also develop polynomial-time algorithms for weighted generalizations where the seminal work of Chen, Kleinberg, Lov\'asz, Rajaraman, Sundaram, and Vetta (JACM'07) on confluent flows established only existential non-constructive results.

cs.DS↗

arXiv2025

Pickle: Precise, Flexible Cross-Core Last-level Cache Data Prefetching for Irregular Memory Accesses

Graph analytics and sparse scientific workloads are dominated by parallel chains of data-dependent, long-latency memory accesses whose patterns are difficult for hardware to infer yet straightforward to express in software. Conventional hardware prefetchers attempt to recover this information from address streams alone, but false positives lead to substantial memory traffic overhead. Software-assisted approaches offer greater flexibility but still consume core limited resources. We propose Pickle, a software-defined, hardware-managed lastlevel cache (LLC) prefetcher that follows the decoupled access/execute philosophy. Pickle serves as an independent access engine, fully decoupled from core resources, that executes prefetch kernels sliced from the original application to bring data into the shared LLC ahead of demand. We evaluate Pickle using full-system, cycle-level simulation of a cluster of 8 high-performance cores, running all GAP benchmark suite algorithms across nine real-world graphs and irregular-access dominated scientific applications from the NAS parallel benchmark suite. Over a no-prefetching baseline, Pickle achieves 1.49x geomean speedup with only 2% DRAM traffic overhead on graph algorithms, and 1.53x with a 4.5% memory traffic reduction on NAS scatter/gather kernels. For reference, the state-of-the-art coreprivate indirect prefetcher achieves 1.40x but incurs 43% DRAM traffic overhead on graph workloads, and 1.36x at zero traffic overhead on scatter/gather kernels, illustrating the challenge of inferring irregular access patterns without application-level context. Pickle also composes transparently with private cache prefetchers: combining it with the state-of-the-art indirect or a simple stride prefetcher yields 1.65x-1.66x and 1.72x-1.84x geomean speedup on graph and NAS scatter/gather workloads, respectively.

cs.AR↗

arXiv2025

Choreographer: A Full-System Framework for Fine-Grained Tasks in Cache Hierarchies

In this paper, we introduce Choreographer, a simulation framework that enables a holistic system-level evaluation of fine-grained accelerators designed for latency-sensitive tasks. Unlike existing frameworks, Choreographer captures all hardware and software overheads in core-accelerator and cache-accelerator interactions, integrating a detailed gem5-based hardware stack featuring an AMBA coherent hub interface (CHI) mesh network and a complete Linux-based software stack. To facilitate rapid prototyping, it offers a C++ application programming interface and modular configuration options. Our detailed cache model provides accurate insights into performance variations caused by cache configurations, which are not captured by other frameworks. The framework is demonstrated through two case studies: a data-aware prefetcher for graph analytics workloads, and a quicksort accelerator. Our evaluation shows that the prefetcher achieves speedups between 1.08x and 1.88x by reducing memory access latency, while the quicksort accelerator delivers more than 2x speedup with minimal address translation overhead. These findings underscore the ability of Choreographer to model complex hardware-software interactions and optimize performance in small task offloading scenarios.

cs.AR↗

arXiv2025

Improved Maximin Share Guarantee for Additive Valuations

The maximin share ($\textsf{MMS}$) is the most prominent share-based fairness notion in the fair allocation of indivisible goods. Recent years have seen significant efforts to improve the approximation guarantees for $\textsf{MMS}$ for different valuation classes, particularly for additive valuations. For the additive setting, it has been shown that for some instances, no allocation can guarantee a factor better than $1-\tfrac{1}{n^4}$ of maximin share value to all agents. However, the best currently known algorithm achieves an approximation guarantee of $\tfrac{3}{4} + \tfrac{3}{3836}$ for $\textsf{MMS}$. In this work, we narrow this gap and improve the best-known approximation guarantee for $\textsf{MMS}$ to $\tfrac{10}{13}$.

cs.GT↗

arXiv2025

Improved Approximate EFX Guarantees for Multigraphs

In recent years, a new line of work in fair allocation has focused on EFX allocations for $(p, q)$-bounded valuations, where each good is relevant to at most $p$ agents, and any pair of agents share at most $q$ relevant goods. For the case $p = 2$ and $q = \infty$, such instances can be equivalently represented as multigraphs whose vertices are the agents and whose edges represent goods, each edge incident to exactly the one or two agents for whom the good is relevant. A recent result of \citet{amanatidis2024pushing} shows that for additive $(2,\infty)$ bounded valuations, a $(\nicefrac{2}{3})$-EFX allocation always exists. In this paper, we improve this bound by proving the existence of a $(\nicefrac{1}{\sqrt{2}})$-$\efx$ allocation for additive $(2,\infty)$-bounded valuations.

cs.GT↗

arXiv2024

Almost Envy-free Allocation of Indivisible Goods: A Tale of Two Valuations

The existence of $\textsf{EFX}$ allocations stands as one of the main challenges in discrete fair division.In this paper, we present symmetrical results on the existence of $\textsf{EFX}$ and its approximate variations for two distinct valuations: restricted additive valuations and $(p,q)$-bounded valuations introduced by Christodoulou \etal \cite{christodoulou2023fair}. In a $(p,q)$-bounded instance, each good has relevance for at most $p$ agents, and any pair of agents shares at most $q$ common relevant goods. We show that instances with $(\infty,1)$-bounded valuations admit $\textsf{EF2X}$ allocations and $\textsf{EFX}$ allocations with at most $\lfloor {n}/{2} \rfloor - 1$ discarded goods, mirroring results for the restricted additive setting \cite{akrami2022ef2x}. We also present ${({\sqrt{2}}/{2})\textsf{-EFX}}$ algorithms for both restricted additive and $(\infty,1)$-bounded subadditive settings. The symmetry of these results suggests these valuations share symmetric structures. Building on this, we propose an $\textsf{EFX}$ allocation for restricted additive valuations when $p=2$ and $q=\infty$. To achieve these results, we further develop the rank concept introduced by Farhadi \etal \cite{farhadi2021almost} and introduce several new concepts such as virtual value, rankpath, and root, which advance the overall understanding of $\textsf{EFX}$ allocations. In addition, we suggest an updating rule based on the virtual values which we believe will lead to broader and more generalized results on $\textsf{EFX}$.

cs.GT↗