arXiv subjects

Sofia Vazquez Alferez

Publications and source records attributed to Sofia Vazquez Alferez.

6 recordsLinked to original sources

arXiv2026

Binary constraints on one additional variable can create exponential ascents for local search

Local search in combinatorial optimisation can be viewed as an uphill climb on a corresponding fitness landscape, where the assignments visited by a strict local search follow an ascent. This hill-climbing is sometimes surprisingly efficient, but not always. Since fitness landscapes can be succinctly represented by Boolean valued constraint satisfaction problems (VCSPs), we ask: what properties of VCSPs ensure that all ascents are polynomial? Or alternatively, what are the "simplest" VCSPs with exponential ascents? Prior examples of VCSPs with exponential ascents were built up as a chain of gadgets of constraints. Here we investigate what happens for simpler starlike graphs. To establish lower bounds on the \emph{longest} ascent, we construct: (1) a star of binary constraints with a quadratic longest ascent, (2) a binary VCSP of treedepth 3 on 4n + 1 Boolean variables (made by gluing 2n triangles of constraints at a common centre variable) with an exponential longest ascent of length $10\cdot2^n - 9$, and (3) starlike VCSP of logarithmic vertex cover number with an exponential longest ascent. For steepest ascent, we prove (4) a tight bound of 2(n - 1) for VCSPs with star constraint graphs, and construct (5) a starlike tree VCSP with treedepth 3 with a quadratic steepest ascent. Finally, we prove upper bounds on the shortest ascent from any initial assignment: (6) linear for VCSPs of treedepth 3; and (7) $O(2^k (n - k))$ for VCSPs of vertex cover number k. Together (2) and (6) establish treedepth 3, and (3) and (7) establish logarithmic vertex cover number, as the first structural graph parameters for which the longest and shortest ascents can be exponentially separated. We discuss the consequences of our results for the parameterized complexity of local search.

cs.DM↗

arXiv2026

Investigation of regional variations in CO$_2$ growth rates : Integrating Emission Inventories and Atmospheric Observations

Atmospheric carbon dioxide (CO2) growth rates reflects the combined influence of anthropogenic emissions, biospheric carbon exchange, and climate variability. While climate mitigation is primarily evaluated using bottom-up emission inventories within political boundaries, there is a need to validate these emission reductions using atmospheric measurements. Here, we present a global top-down analysis of atmospheric CO2 growth rates using CAMS atmospheric CO2 reanalysis, EDGAR anthropogenic emissions, GOSIF dataset and the Southern Oscillation Index (SOI) as a measures of biospheric activity, to quantify the relative influence of human and natural drivers. We find that atmospheric CO2 growth rate varies substantially across space and time but is dominated by natural carbon-cycle processes and global background trends. Anthropogenic emission signals are frequently masked by natural variability, making regional top-down detection of human emission changes difficult. The COVID-19 emission reductions in 2020, despite occurring during a neutral ENSO year, were not consistently reflected in regional atmospheric CO2 growth rates, highlighting the dominant roles of biospheric dynamics and atmospheric transport. Using unsupervised clustering and persistence analysis, we identify five characteristic carbon-cycle regimes. Spatial averaging removes much of the regional variability, leaving large-scale climate as the dominant control in most regimes. The active biosphere is the main exception, where strong biogenic signals persist, underscoring the critical role of tropical forests in shaping atmospheric CO2 variability.

physics.ao-ph↗

arXiv2026

When is local search both effective and efficient?

Combinatorial optimization problems implicitly define fitness landscapes that combine the numeric structure of the 'fitness' function to be maximized with the combinatorial structure of which assignments are 'adjacent'. Local search starts at an assignment in this landscape and successively moves assignments until no further improvement is possible among the adjacent assignments. Classic analyses of local search algorithms have focused more on the question of effectiveness ("did we find a good solution?") and often implicitly assumed that there are no doubts about their efficiency ("did we find it quickly?"). But there are many reasons to doubt the efficiency of local search. Even if we focus on fitness landscapes on the hypercube that are single peaked on every subcube (i.e., semismooth fitness landscapes) where effectiveness is obvious, many local search algorithms are known to be inefficient. Since fitness landscapes are unwieldy exponentially large objects, we focus on their polynomial-sized representations by instances of valued constraint satisfaction problems (VCSP). We define a "direction" for valued constraints such that directed VCSPs generate semismooth fitness landscapes. We call VCSPs oriented if they do not have any pair of variables with arcs in both directions. Since recognizing if a VCSP-instance is directed or oriented is coNP-complete, we generalized oriented VCSPs as conditionally-smooth fitness landscapes that are recognizable in polynomial time for a VCSP-instance. We prove that many popular local search algorithms like random ascent, simulated annealing, history-based rules, jumping rules, and the Kernighan-Lin heuristic are very efficient on conditionally-smooth landscapes. But conditionally-smooth landscapes are still expressive enough so that algorithms like steepest ascent and random facet require a super-polynomial number of steps to find the fitness peak.

cs.DS↗

arXiv2025

A strengthened bound on the number of states required to characterize maximum parsimony distance

In this article we prove that the distance $d_{\mathrm{MP}}(T_1,T_2) = k$ between two unrooted binary phylogenetic trees $T_1, T_2$ on the same set of taxa can be defined by a character that is convex on one of $T_1, T_2$ and which has at most $2k$ states. This significantly improves upon the previous bound of $7k-5$ states. We also show that for every $k \geq 1$ there exist two trees $T_1, T_2$ with $d_{\mathrm{MP}}(T_1,T_2) = k$ such that at least $k+1$ states are necessary in any character that achieves this distance and which is convex on one of $T_1, T_2$. We augment these lower and upper bounds with an empirical analysis which shows that in practice significantly fewer than $k+1$ states are usually required.

q-bio.PE↗

arXiv2025

Greed is slow on sparse graphs of oriented valued constraints

Greedy local search is especially popular for solving valued constraint satisfaction problems (VCSPs). Since any method will be slow for some VCSPs, we ask: what is the simplest VCSP on which greedy local search is slow? We construct a VCSP on 6n Boolean variables for which greedy local search takes 7(2^n - 1) steps to find the unique peak. Our VCSP is simple in two ways. First, it is very sparse: its constraint graph has pathwidth 2 and maximum degree 3. This is the simplest VCSP on which some local search could be slow. Second, it is "oriented" - there is an ordering on the variables such that later variables are conditionally-independent of earlier ones. Being oriented allows many non-greedy local search methods to find the unique peak in a quadratic number of steps. Thus, we conclude that - among local search methods - greed is particularly slow.

cs.DM↗

arXiv2024

Destroying Densest Subgraphs is Hard

We analyze the computational complexity of the following computational problems called Bounded-Density Edge Deletion and Bounded-Density Vertex Deletion: Given a graph $G$, a budget $k$ and a target density $τ_ρ$, are there $k$ edges ($k$ vertices) whose removal from $G$ results in a graph where the densest subgraph has density at most $τ_ρ$? Here, the density of a graph is the number of its edges divided by the number of its vertices. We prove that both problems are polynomial-time solvable on trees and cliques but are NP-complete on planar bipartite graphs and split graphs. From a parameterized point of view, we show that both problems are fixed-parameter tractable with respect to the vertex cover number but W[1]-hard with respect to the solution size. Furthermore, we prove that Bounded-Density Edge Deletion is W[1]-hard with respect to the feedback edge number, demonstrating that the problem remains hard on very sparse graphs.

cs.DS↗