arXiv AI
Aug 5
EFX Allocation In (Multi)Hypergraphs
arXiv:2608. 03171v1 Announce Type: cross Abstract: We study fair allocations of indivisible goods among agents with heterogeneous monotone valuations.
Independence-System Realisations in Single-Source Unsplittable Flow
The paper introduces a path‑closed framework for realizing independence systems via zero‑cost choices of primary terminals in directed acyclic flow instances, extending the triangle mechanism to all finite loopless independence systems. It shows that such systems, including all finite simple graphs and hypergraph independence systems without singleton forbidden hyperedges, admit polynomial‑size realizations measured by the incidence size of minimal forbidden sets. The authors further specialize to odd cycles, deriving a rational family that yields a fractional cheap‑selection vector violating the odd‑cycle inequality and establishing an exact additive‑congestion threshold that approaches 1/2 for large cycles.
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arXiv AI
Aug 21
FMT$^{\mathrm{X}}$: Lazy Wavefront Search for Dynamic Replanning
arXiv:2509. 08521v2 Announce Type: replace-cross Abstract: FMT$^{*}$ plans efficiently in static worlds by expanding a cost-ordered wavefront and collision-checking lazily, but its single-pass unvisited rule cannot revise paths when obstacles change.
arXiv AI
Jul 28
Formalizing Flag Algebras in Lean
arXiv:2607. 23500v1 Announce Type: cross Abstract: Razborov's flag algebra method is a powerful tool for proving asymptotic inequalities in extremal graph theory, often reducing the task to finding a finite certificate by semidefinite programming.
arXiv Machine Learning
Jul 21
The Dimension of Nonterminating Resampling Computations
arXiv:2607. 17469v1 Announce Type: cross Abstract: A randomized algorithm may terminate almost surely even though exceptional random tapes make it run forever.
arXiv AI
Jul 14
Instruction Set and Language for Hypergraphs
arXiv:2607. 10194v1 Announce Type: cross Abstract: We present IsalHG, a method for representing the structure of any finite, connected hypergraph of bounded hyperedge arity as a string over a compact instruction alphabet $\Sigma_{\mathrm{HG}}$.
arXiv Machine Learning
Sep 1
Strengthening Recursive Constructions for Zero-Error Shannon Capacity
arXiv:2608. 30273v1 Announce Type: cross Abstract: The exact Shannon capacity is unknown for every odd cycle beyond the five-cycle $C_5$, making odd cycles a central open problem in zero-error information theory.
arXiv AI
Jul 31
Pushing the Frontier on Approximate EFX Allocations
arXiv:2406. 12413v3 Announce Type: replace-cross Abstract: We study the problem of allocating a set of indivisible goods to a set of agents with additive valuation functions, aiming to achieve approximate envy-freeness up to any good ($\alpha$-EFX).
arXiv Machine Learning
Jul 23
Hard Guarantees at a Measured Price: Entropy-Stable Learned Finite Volumes for Compressible Flow
arXiv:2607. 20171v1 Announce Type: cross Abstract: Learned solvers for compressible flow are usually compared to classical methods at equal mesh resolution rather than at equal computational cost, and they typically offer no guarantee that their solutions remain physically admissible.
arXiv Machine Learning
Sep 2
Fair Minimum Labeling: Efficient Temporal Network Activations for Reachability and Equity
arXiv:2510.03899v3 Announce Type: replace-cross Abstract: Balancing resource efficiency and fairness is critical in networked systems that support modern learning applications. We introduce the \emph...
arXiv AI
Jul 24
Improved lower bounds for the Shannon capacity of odd cycles
arXiv:2607. 21517v1 Announce Type: cross Abstract: The Shannon capacity $\Theta(G)$ of a graph $G$ quantifies the maximum rate at which information can be transmitted with zero error over a noisy channel.
arXiv AI
Aug 13
A Forced-Structure Reduction and Verifiable Bounds for Conway's 99-Graph
arXiv:2608. 11211v1 Announce Type: new Abstract: Conway's 99-graph problem asks whether a strongly regular graph with parameters $\mathrm{srg}(99,14,1,2)$ exists.
arXiv Machine Learning
Sep 24
Binary Quantized Neural Network Training Is W[1]-Hard Parameterized by Input and Output Dimensions
The paper proves that training a binary quantized neural network (2-QNNT) is W[1]-hard when parameterized solely by the sum of input and output dimensions, α+ω. This hardness result holds even for zero training error on a specially constructed dataset where each input equals its target and the examples form a coordinate‑wise prefix chain. The proof reduces from DAG edge‑disjoint paths, employing a one‑flip routing equivalence that links activation transitions to vertex‑disjoint paths in the network.