Long-horizon LLM agents require memory systems that remain accurate under fixed context budgets. However, existing systems struggle with two persistent challenges in long-term dialogue: (i) \textbf{disconnected evidence}, where multi-hop answers require linking facts distributed across time, and (ii) \textbf{state updates}, where evolving information (e.g., schedule changes) creates conflicts with older static logs. We propose AriadneMem, a structured memory system that addresses these failure modes via a decoupled two-phase pipeline. In the \textbf{offline construction phase}, AriadneMem employs \emph{entropy-aware gating} to filter noise and low-information message before LLM extraction and applies \emph{conflict-aware coarsening} to merge static duplicates while preserving state transitions as temporal edges. In the \textbf{online reasoning phase}, rather than relying on expensive iterative planning, AriadneMem executes \emph{algorithmic bridge discovery} to reconstruct missing logical paths between retrieved facts, followed by \emph{single-call topology-aware synthesis}. On LoCoMo experiments with GPT-4o, AriadneMem improves \textbf{Multi-Hop F1 by 15.2\%} and \textbf{Average F1 by 9.0\%} over strong baselines. Crucially, by offloading reasoning to the graph layer, AriadneMem reduces \textbf{total runtime by 77.8\%} using only \textbf{497} context tokens. The code is available at https://github.com/LLM-VLM-GSL/AriadneMem.